Gohberg, I. (Israel) 19282009
Overview
Works:  306 works in 1,483 publications in 4 languages and 24,010 library holdings 

Genres:  Conference papers and proceedings Archives History 
Roles:  Author, Editor, Honoree, Other, htt 
Classifications:  QA320, 515.724 
Publication Timeline
.
Most widely held works about
I Gohberg
 A panorama of modern operator theory and related topics : the Israel Gohberg memorial volume by H Dym( )
 Israel Gohberg and friends : on the occasion of his 80th birthday by H Bart( Book )
Most widely held works by
I Gohberg
Israel Gohberg and friends : on the occasion of his 80th birthday by
H Bart(
)
10 editions published in 2008 in English and held by 784 WorldCat member libraries worldwide
This book is dedicated to Israel Gohberg on occasion of his 80th birthday on August 23, 2008. It is an expression of esteem and friendship for a great mathematician, a remarkable person and an inspiring colleague. The book contains reflections by Gohberg himself on his own mathematical activities and those of others. It also includes contributions of colleagues and coworkers, both from his time in the Soviet Union and from when he lived and worked in the West. The contributions in question are not mathematical research papers but focus on the man Israel Gohberg and are intended for a wide audience. To be found are letters, speeches, laudatios and reminiscences which, together, present an attractive picture of the way in which Israel Gohberg in the past four to five decades influenced the lives of many mathematicians. Biographical material such as a curriculum vitae, a list of publications, a list of Ph. D. students and information about honorary doctoral degrees is also included
10 editions published in 2008 in English and held by 784 WorldCat member libraries worldwide
This book is dedicated to Israel Gohberg on occasion of his 80th birthday on August 23, 2008. It is an expression of esteem and friendship for a great mathematician, a remarkable person and an inspiring colleague. The book contains reflections by Gohberg himself on his own mathematical activities and those of others. It also includes contributions of colleagues and coworkers, both from his time in the Soviet Union and from when he lived and worked in the West. The contributions in question are not mathematical research papers but focus on the man Israel Gohberg and are intended for a wide audience. To be found are letters, speeches, laudatios and reminiscences which, together, present an attractive picture of the way in which Israel Gohberg in the past four to five decades influenced the lives of many mathematicians. Biographical material such as a curriculum vitae, a list of publications, a list of Ph. D. students and information about honorary doctoral degrees is also included
Basic operator theory by
I Gohberg(
Book
)
27 editions published between 1980 and 2013 in English and Undetermined and held by 715 WorldCat member libraries worldwide
Rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems, except for the last chapter which is an introduction to the theory of nonlinear operators. In addition to the standard topics in functional anal ysis, we have presented relatively recent results which appear, for example, in Chapter VII. In general, in writ ing this book, the authors were strongly influenced by re cent developments in operator theory which affected the choice of topics, proofs and exercises. One of the main features of this book is the large number of new exercises chosen to expand the reader's com prehension of the material, and to train him or her in the use of it. In the beginning portion of the book we offer a large selection of computational exercises; later, the proportion of exercises dealing with theoretical questions increases. We have, however, omitted exercises after Chap ters V, VII and XII due to the specialized nature of the subject matter
27 editions published between 1980 and 2013 in English and Undetermined and held by 715 WorldCat member libraries worldwide
Rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems, except for the last chapter which is an introduction to the theory of nonlinear operators. In addition to the standard topics in functional anal ysis, we have presented relatively recent results which appear, for example, in Chapter VII. In general, in writ ing this book, the authors were strongly influenced by re cent developments in operator theory which affected the choice of topics, proofs and exercises. One of the main features of this book is the large number of new exercises chosen to expand the reader's com prehension of the material, and to train him or her in the use of it. In the beginning portion of the book we offer a large selection of computational exercises; later, the proportion of exercises dealing with theoretical questions increases. We have, however, omitted exercises after Chap ters V, VII and XII due to the specialized nature of the subject matter
Indefinite linear algebra and applications by
I Gohberg(
)
26 editions published in 2005 in English and Undetermined and held by 632 WorldCat member libraries worldwide
"The book has the structure of a graduate text in which chapters on advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike."
26 editions published in 2005 in English and Undetermined and held by 632 WorldCat member libraries worldwide
"The book has the structure of a graduate text in which chapters on advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike."
Matrix polynomials by
I Gohberg(
Book
)
35 editions published between 1982 and 2009 in 3 languages and held by 631 WorldCat member libraries worldwide
This book provides a comprehensive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the WienerHopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials. Audience: students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduatelevel courses in linear algebra and complex analysis
35 editions published between 1982 and 2009 in 3 languages and held by 631 WorldCat member libraries worldwide
This book provides a comprehensive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the WienerHopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials. Audience: students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduatelevel courses in linear algebra and complex analysis
Invariant subspaces of matrices with applications by
I Gohberg(
Book
)
30 editions published between 1986 and 2006 in English and held by 595 WorldCat member libraries worldwide
This unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions. Audience: appropriate for students, instructors, and researchers in applied linear algebra, linear systems theory, and signal processing. Its contents are accessible to readers who have had undergraduatelevel courses in linear algebra and complex function theory
30 editions published between 1986 and 2006 in English and held by 595 WorldCat member libraries worldwide
This unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions. Audience: appropriate for students, instructors, and researchers in applied linear algebra, linear systems theory, and signal processing. Its contents are accessible to readers who have had undergraduatelevel courses in linear algebra and complex function theory
The state space method : generalizations and applications by
Daniel Alpay(
)
18 editions published between 2005 and 2006 in English and German and held by 562 WorldCat member libraries worldwide
"The state space method developed in the last decades allows us to study the theory of linear systems by using tools from the theory of linear operators; conversely, it had a strong influence on operator theory introducing new questions and topics." "The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations." "The articles in the volume will be of interest to pure and applied mathematicians, electrical engineers and theoretical physicists."Jacket
18 editions published between 2005 and 2006 in English and German and held by 562 WorldCat member libraries worldwide
"The state space method developed in the last decades allows us to study the theory of linear systems by using tools from the theory of linear operators; conversely, it had a strong influence on operator theory introducing new questions and topics." "The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations." "The articles in the volume will be of interest to pure and applied mathematicians, electrical engineers and theoretical physicists."Jacket
Holomorphic operator functions of one variable and applications : methods from complex analysis in several variables by
I Gohberg(
)
19 editions published in 2009 in English and held by 523 WorldCat member libraries worldwide
This is a book on holomorphic operator functions of a single variable and applications, which is focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables. The first part of the theory starts with a straightforward generalization of some results from the basics of analysis of scalar functions of one complex variable. In the second part, which is the main part of the theory, results are obtained by methods and tools adapted from complex analysis of functions of several variables. We have in mind the theory of holomorphic cocycles (fiber bundles) with values in infinitedimensional noncommutative groups. As a rule, these results do not appear in traditional complex analysis of one variable, not even for matrix valued cocycles. The third part consists of applications to operator theory. Here applications are presented for holomorphic families of subspaces and PlemeljMuschelishvili factorization. The fourth part presents a generalization of the theory of cocycles to cocycles with restrictions. This part contains also applications to interpolation problems, to the problem of holomorphic equivalence and diagonalization
19 editions published in 2009 in English and held by 523 WorldCat member libraries worldwide
This is a book on holomorphic operator functions of a single variable and applications, which is focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables. The first part of the theory starts with a straightforward generalization of some results from the basics of analysis of scalar functions of one complex variable. In the second part, which is the main part of the theory, results are obtained by methods and tools adapted from complex analysis of functions of several variables. We have in mind the theory of holomorphic cocycles (fiber bundles) with values in infinitedimensional noncommutative groups. As a rule, these results do not appear in traditional complex analysis of one variable, not even for matrix valued cocycles. The third part consists of applications to operator theory. Here applications are presented for holomorphic families of subspaces and PlemeljMuschelishvili factorization. The fourth part presents a generalization of the theory of cocycles to cocycles with restrictions. This part contains also applications to interpolation problems, to the problem of holomorphic equivalence and diagonalization
Recent advances in operator theory and its applications : the Israel Gohberg anniversary volume : International Workshop on
Operator Theory and its Applications, IWOTA 2003, Cagliari, Italy by
I Gohberg(
)
17 editions published in 2005 in English and held by 516 WorldCat member libraries worldwide
Thisvolumecontainsaselectionofpapersinmodernoperatortheoryanditsapp cations. Most of them are directly related to lectures presented at the Fourteenth International Workshop on Operator Theory and its Applications (IWOTA 2003) held at the University of Cagliari, Italy, in the period of June 2427, 2003. The workshop, which was attended by 108 mathematicians  including a number of PhD and postdoctoral students  from 22 countries, presented eight special sessions on 1) control theory, 2) interpolation theory, 3) inverse scattering, 4) numerical estimates for operators, 5) numerical treatment of integral equations, 6) pseudodi?erential operators, 7) realizations and transformations of analytic functions and inde?nite inner product spaces, and 8) structured matrices. The program consisted of 19 plenary lectures of 45 minutes and 78 lectures of 30 minutes in four parallel sessions. The present volume re?ects the wide range and rich variety of topics p sentedanddiscussedattheworkshop,bothwithinandoutsidethespecialsessions. The papers deal with inverse scattering, numerical ranges, pseudodi?erential  erators, numerical analysis, interpolation theory, multidimensional system theory, inde?nite inner products, spectral factorization, and stationary processes. SinceintheperiodthattheproceedingsofIWOTA2003werebeingprepared, Israel Gohberg, the president of the IWOTA steering committee, reached the age of 75, we decided to dedicate these proceedings to Israel Gohberg on the occasion of his 75th birthday. All of the authors of these proceedingshavejoined the editors and dedicated their papers to him as well
17 editions published in 2005 in English and held by 516 WorldCat member libraries worldwide
Thisvolumecontainsaselectionofpapersinmodernoperatortheoryanditsapp cations. Most of them are directly related to lectures presented at the Fourteenth International Workshop on Operator Theory and its Applications (IWOTA 2003) held at the University of Cagliari, Italy, in the period of June 2427, 2003. The workshop, which was attended by 108 mathematicians  including a number of PhD and postdoctoral students  from 22 countries, presented eight special sessions on 1) control theory, 2) interpolation theory, 3) inverse scattering, 4) numerical estimates for operators, 5) numerical treatment of integral equations, 6) pseudodi?erential operators, 7) realizations and transformations of analytic functions and inde?nite inner product spaces, and 8) structured matrices. The program consisted of 19 plenary lectures of 45 minutes and 78 lectures of 30 minutes in four parallel sessions. The present volume re?ects the wide range and rich variety of topics p sentedanddiscussedattheworkshop,bothwithinandoutsidethespecialsessions. The papers deal with inverse scattering, numerical ranges, pseudodi?erential  erators, numerical analysis, interpolation theory, multidimensional system theory, inde?nite inner products, spectral factorization, and stationary processes. SinceintheperiodthattheproceedingsofIWOTA2003werebeingprepared, Israel Gohberg, the president of the IWOTA steering committee, reached the age of 75, we decided to dedicate these proceedings to Israel Gohberg on the occasion of his 75th birthday. All of the authors of these proceedingshavejoined the editors and dedicated their papers to him as well
Interpolation, Schur functions, and moment problems by
Daniel Alpay(
)
10 editions published in 2006 in English and held by 494 WorldCat member libraries worldwide
Schur analysis originates with a 1917 paper by Schur where he associated to a function analytic and contractive in the open unit disk a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often called reflection coefficients. Under the word Schur analysis one encounters a variety of problems related to Schur functions such as interpolation problems, moment problems, study of the relationships between the Schur coefficients and the properties of the function, study of underlying operators and others. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes
10 editions published in 2006 in English and held by 494 WorldCat member libraries worldwide
Schur analysis originates with a 1917 paper by Schur where he associated to a function analytic and contractive in the open unit disk a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often called reflection coefficients. Under the word Schur analysis one encounters a variety of problems related to Schur functions such as interpolation problems, moment problems, study of the relationships between the Schur coefficients and the properties of the function, study of underlying operators and others. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes
Introduction to the theory of linear nonselfadjoint operators by
I Gohberg(
Book
)
25 editions published between 1969 and 1988 in English and held by 485 WorldCat member libraries worldwide
25 editions published between 1969 and 1988 in English and held by 485 WorldCat member libraries worldwide
Results and problems in combinatorial geometry by
V. G Bolti︠a︡nskiĭ(
Book
)
22 editions published between 1965 and 1986 in English and Russian and held by 465 WorldCat member libraries worldwide
In this short book, the authors discuss three types of problems from combinatorial geometry: Borsuk's partition problem, covering convex bodies by smaller homothetic bodies, and the illumination problem. They show how closely related these problems are to each other. The presentation is elementary, with no more than highschool mathematics and an interest in geometry required to follow the arguments. Most of the discussion is restricted to two and threedimensional Euclidean space, though sometimes more general results and problems are given. Thus even the mathematically unsophisticated reader can grasp some of the results of a branch of twentiethcentury mathematics that has applications in such disciplines as mathematical programming, operations research and theoretical computer science. At the end of the book the authors have collected together a set of unsolved and partially solved problems that a sixthform student should be able to understand and even attempt to solve
22 editions published between 1965 and 1986 in English and Russian and held by 465 WorldCat member libraries worldwide
In this short book, the authors discuss three types of problems from combinatorial geometry: Borsuk's partition problem, covering convex bodies by smaller homothetic bodies, and the illumination problem. They show how closely related these problems are to each other. The presentation is elementary, with no more than highschool mathematics and an interest in geometry required to follow the arguments. Most of the discussion is restricted to two and threedimensional Euclidean space, though sometimes more general results and problems are given. Thus even the mathematically unsophisticated reader can grasp some of the results of a branch of twentiethcentury mathematics that has applications in such disciplines as mathematical programming, operations research and theoretical computer science. At the end of the book the authors have collected together a set of unsolved and partially solved problems that a sixthform student should be able to understand and even attempt to solve
Theory and applications of Volterra operators in Hilbert space by
I Gohberg(
Book
)
21 editions published between 1970 and 2004 in English and held by 455 WorldCat member libraries worldwide
21 editions published between 1970 and 2004 in English and held by 455 WorldCat member libraries worldwide
Topics in operator theory : proceedings of the 19th International Workshop on Operator Theory and its Applications, College
of William and Mary, 2008 ; a tribute to Israel Gohberg on the occasion of his 80th birthday by International Workshop on Operator Theory and Applications(
)
26 editions published in 2010 in English and German and held by 428 WorldCat member libraries worldwide
This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications
26 editions published in 2010 in English and German and held by 428 WorldCat member libraries worldwide
This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications
Convolution equations and projection methods for their solution by
I Gohberg(
Book
)
18 editions published between 1974 and 2005 in English and held by 382 WorldCat member libraries worldwide
18 editions published between 1974 and 2005 in English and held by 382 WorldCat member libraries worldwide
Traces and determinants of linear operators by
I Gohberg(
Book
)
15 editions published in 2000 in English and held by 340 WorldCat member libraries worldwide
"The authors initially planned to write an article describing the origins and developments of the theory of Fredholm operators and to present their recollections of this topic. We started to read again classical papers and we were sidetracked by the literature concerned with the theory and applications of traces and determinants of infinite matrices and integral operators. We were especially impressed by the papers of Poincare, von Koch, Fredholm, Hilbert and Carleman, as well as F. Riesz's book on infinite systems of linear equations. Consequently our plans were changed and we decided to write a paper on the history of determinants of infinite matrices and operators. During the preparation of our paper we realized that many mathematical questions had to be answered in order to gain a more complete understanding of the subject. So, we changed our plans again and decided to present the subject in a more advanced form which would satisfy our new requirements. This whole process took between four and five years of challenging, but enjoyable work. This entailed the study of the appropriate relatively recent results of Grothendieck, Ruston, Pietsch, Hermann Konig and others. After the papers [GGK1] and [GGK2] were published, we saw that the written material could serve as the basis of a book."The authors
15 editions published in 2000 in English and held by 340 WorldCat member libraries worldwide
"The authors initially planned to write an article describing the origins and developments of the theory of Fredholm operators and to present their recollections of this topic. We started to read again classical papers and we were sidetracked by the literature concerned with the theory and applications of traces and determinants of infinite matrices and integral operators. We were especially impressed by the papers of Poincare, von Koch, Fredholm, Hilbert and Carleman, as well as F. Riesz's book on infinite systems of linear equations. Consequently our plans were changed and we decided to write a paper on the history of determinants of infinite matrices and operators. During the preparation of our paper we realized that many mathematical questions had to be answered in order to gain a more complete understanding of the subject. So, we changed our plans again and decided to present the subject in a more advanced form which would satisfy our new requirements. This whole process took between four and five years of challenging, but enjoyable work. This entailed the study of the appropriate relatively recent results of Grothendieck, Ruston, Pietsch, Hermann Konig and others. After the papers [GGK1] and [GGK2] were published, we saw that the written material could serve as the basis of a book."The authors
Minimal factorization of matrix and operator functions by
H Bart(
Book
)
13 editions published in 1979 in English and Undetermined and held by 339 WorldCat member libraries worldwide
13 editions published in 1979 in English and Undetermined and held by 339 WorldCat member libraries worldwide
Factorization of matrix functions and singular integral operators by
Kevin Clancey(
Book
)
15 editions published between 1198 and 2013 in English and German and held by 330 WorldCat member libraries worldwide
A few years aga the authors started a project of a book on the theory of systems of onedimensional singular integral equaƯ tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik ̃̃ concerning scalar equaƯ tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions visavis appliƯ cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is of independent interest and we decided to publish this chapter as aseparate volume. In fact, because of recent activity, the amount of material was quite large and we quickly learned that we cannot cover all of the results in complete detail. We have tried to include a represenƯ tative variety of all kinds of methods, techniques, results and applications. Apart of the current work exposes results from the Russian literature which have never appeared in English translation. We have also decided to reflect some of the recent results which make interesting connections between factorization of matrix functions and systems theory. The field remains very active and many results and connecƯ tions are still not weIl understood. These notes should be viewed as a stepping stone to further development. The authors hope that sometime they will return to complete their original plan
15 editions published between 1198 and 2013 in English and German and held by 330 WorldCat member libraries worldwide
A few years aga the authors started a project of a book on the theory of systems of onedimensional singular integral equaƯ tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik ̃̃ concerning scalar equaƯ tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions visavis appliƯ cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is of independent interest and we decided to publish this chapter as aseparate volume. In fact, because of recent activity, the amount of material was quite large and we quickly learned that we cannot cover all of the results in complete detail. We have tried to include a represenƯ tative variety of all kinds of methods, techniques, results and applications. Apart of the current work exposes results from the Russian literature which have never appeared in English translation. We have also decided to reflect some of the recent results which make interesting connections between factorization of matrix functions and systems theory. The field remains very active and many results and connecƯ tions are still not weIl understood. These notes should be viewed as a stepping stone to further development. The authors hope that sometime they will return to complete their original plan
Topics in functional analysis : essays dedicated to M.G. Krein on the occasion of his 70th birthday by
M. G Kreĭn(
Book
)
19 editions published in 1978 in English and held by 324 WorldCat member libraries worldwide
19 editions published in 1978 in English and held by 324 WorldCat member libraries worldwide
Classes of linear operators by
I Gohberg(
Book
)
16 editions published between 1993 and 2013 in English and German and held by 323 WorldCat member libraries worldwide
This book presents a panorama of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. This second volume consists of five parts: triangular representations, classes of Toeplitz operators, contractive operators and characteristic operator functions, Banach algebras and algebras of operators, and extension and completion problems. The exposition is selfcontained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering. Contents: Vol. I  This book presents a panorama of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. The present volume consists of four parts: general spectral theory, classes of compact operators, Fredholm and WienerHopf operators, and classes of unbounded operators: The exposition is selfcontained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering." ... Used as a graduate textbook, the book allows the instructor several good selections of topics to build a course. ... The authors took great care to polish and simplify the exposition; as a result, the book can serve also as an excellent basis for reading courses or for selfstudy. ... Besides being a textbook, the book is a valuable reference source for a wide audience of mathematicians, physicists and engineers. The specialists in functional analysis and operator theory will find most of the topics familiar, although the exposition is often novel or nontraditional, making the material more accessible. ..." (Zentralblatt für Mathematik) / "This book presents an excellently chosen panorama of operator theory. It shows for several times the fruitful application of complex analysis to problems in operator theory. ... Each part contains interesting exercises and comments on the literature of the topic." (Monatshefte für Mathematik)
16 editions published between 1993 and 2013 in English and German and held by 323 WorldCat member libraries worldwide
This book presents a panorama of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. This second volume consists of five parts: triangular representations, classes of Toeplitz operators, contractive operators and characteristic operator functions, Banach algebras and algebras of operators, and extension and completion problems. The exposition is selfcontained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering. Contents: Vol. I  This book presents a panorama of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. The present volume consists of four parts: general spectral theory, classes of compact operators, Fredholm and WienerHopf operators, and classes of unbounded operators: The exposition is selfcontained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering." ... Used as a graduate textbook, the book allows the instructor several good selections of topics to build a course. ... The authors took great care to polish and simplify the exposition; as a result, the book can serve also as an excellent basis for reading courses or for selfstudy. ... Besides being a textbook, the book is a valuable reference source for a wide audience of mathematicians, physicists and engineers. The specialists in functional analysis and operator theory will find most of the topics familiar, although the exposition is often novel or nontraditional, making the material more accessible. ..." (Zentralblatt für Mathematik) / "This book presents an excellently chosen panorama of operator theory. It shows for several times the fruitful application of complex analysis to problems in operator theory. ... Each part contains interesting exercises and comments on the literature of the topic." (Monatshefte für Mathematik)
Separable type representations of matrices and fast algorithms by
Yuli Eidelman(
)
15 editions published between 2013 and 2014 in English and held by 310 WorldCat member libraries worldwide
This twovolume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The second volume, consisting of four parts, addresses the eigenvalue problem for matrices with quasiseparable structure and applications to the polynomial root finding problem. In the first part the properties of the characteristic polynomials of principal leading submatrices, the structure of eigenspaces and the basic methods for computing eigenvalues are studied in detail for matrices with quasiseparable representation of the first order. The second part is devoted to the divide and conquer method, with the main algorithms also being derived for matrices with quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable representations of any order is studied in the third part. This method is then used in the last part in order to provide a fast solver for the polynomial root finding problem. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike
15 editions published between 2013 and 2014 in English and held by 310 WorldCat member libraries worldwide
This twovolume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The second volume, consisting of four parts, addresses the eigenvalue problem for matrices with quasiseparable structure and applications to the polynomial root finding problem. In the first part the properties of the characteristic polynomials of principal leading submatrices, the structure of eigenspaces and the basic methods for computing eigenvalues are studied in detail for matrices with quasiseparable representation of the first order. The second part is devoted to the divide and conquer method, with the main algorithms also being derived for matrices with quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable representations of any order is studied in the third part. This method is then used in the last part in order to provide a fast solver for the polynomial root finding problem. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike
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Related Identities
 Kaashoek, M. A. Other Editor
 Rodman, L. Other Author Editor
 Lancaster, Peter 1929 Other Editor
 Bart, H. (Harm) 1942 Other Author Editor
 Kreĭn, M. G. (Mark Grigorʹevich) 19071989 Editor Honoree Author Dedicatee
 Goldberg, Seymour 1928
 Alpay, Daniel Other Author Editor
 Dym, H. (Harry) 1938 Other Honoree Author Editor
 Krupnik, N. I︠A︡ (Naum I︠A︡kovlevich) 1932
 Bolti︠a︡nskiĭ, V. G. (Vladimir Grigorʹevich) 19252019 Author
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Associated Subjects
Algebra Algebras, Linear Algorithms Analytic spaces Convex domains Convolutions (Mathematics) Determinants Differential equations Differential equations, Partial Factorization (Mathematics) Fourier analysis Free probability theory Friendship Functional analysis Functions of complex variables Functions of several complex variables Geometry, Solid Gohberg, I.(Israel), Hankel operators Hilbert space Holomorphic functions Indefinite inner product spaces Integral equations Integral equationsNumerical solutions Integral operators Interpolation Invariant subspaces Inverse problems (Differential equations) Kreĭn, M. G.(Mark Grigorʹevich), Kyrgyzstan Linear operators Mathematical physics Mathematicians Mathematics Matrices Moment problems (Mathematics) Nonselfadjoint operators Numerical analysis Operator algebras Operator theory Operatorvalued functions Polynomials Schur functions Science Selfadjoint operators Soviet Union Statespace methods Toeplitz operators Volterra operators WienerHopf operators
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Alternative Names
Goberg
Goberg, I.C.
Goberg, I. C., 19282009
Goberg, Israel
Gochberg, I., 19282009
Gochberg I. C.
Gochberg I. C. 19282009
Gochberg, I.Ts 1928
Gochberg, I. Z.
Gochberg, I.Z. 1928
Gochberg, I. Z. 19282009
Gochberg, I. Z. (Israel), 19282009
Gochberg, Izraël
Gochberg, Izraelʹ Cudikovič 19282009
Gochberg, Izrailʹ C. 19282009
Gochberg, Izrailʹ Čudikovič 19282009
Gochberg, Izrail Dudikovic, 19282009
Gochberg, Izrelʹ Cudikovič 19282009
Gochberg, L. Z., 19282009
Gohberg I.
Gohberg, I. 1928
Gohberg I. 19282009
Gohberg, I.C.
Gohberg, I.C. 1928
Gohberg, I. C. 19282009
Gohberg, I. C. (Israel), 19282009
Gohberg, I. (Israel)
Gohberg, I. (Israel), 1928
Gohberg, I. (Israel), 19282009
Gohberg, I. Ts.
Gohberg, I. Z.
Gohberg, Israel
Gohberg, Israel 1928
Gohberg, Israel 19282009
Gohberg, Israel C.
Gohberg, Israel Tschudikowitsch 19282009
Gohberg, Israel' Tsudikovich 1928
Gohberg, Israil 19282009
Gohberg, Izraelʹ Tsudikovich 19282009
Gohberg, Izrail
Gohberg, Izrailʾ 19282009
Gohberg, Izrailʹ C. 19282009
Gohberg, Izrailʹ Cadikovič
Gohberg Izrailʹ Cadikovič 19282009
Gohberg, Izrail' Cudikovič.
Gohberg, Izrailʹ Cudikovič, 1928
Gohberg, Izrailʹ Cudikovič, 19282009
Gohberg, IzrailT︠sudikovic̆
Gohberg, Izrailʹ Tsudikovich
Gohberg, Izrailʹ Tsudikovich, 19282009
Gohberg, Izrail'Tsudikovich 19282009
Gohberg, Iztrail' Tsudikovich 19282009
Gôḥberg, Yiśrāʾēl 19282009
Gohberg, Yiśrāʻēl Z., 19282009
Gokhberg, I.
Gokhberg, I. Ts.
Gokhberg, I. T︠S︡. 1928
Gokhberg, I. T︠S︡. 19282009
Gokhberg, I. T︠S︡. (Izrailʹ T︠S︡udikovich)
Gokhberg, I. T︠S︡. (Izrailʹ T︠S︡udikovich), 1928
Gokhberg, I. T︠S︡. (Izrailʹ T︠S︡udikovich), 19282009
Gokhberg, Izrailʹ T. 19282009
Gokhberg, Izrailʹ T︠S︡udikovich.
Gokhberg, Izrail' Tsudikovich 1923
Gokhberg, Izrailʹ T︠S︡udikovich 1928
Gokhberg, Izrailʹ T︠S︡udikovich 19282008
Gokhberg, Izrailʹ T︠S︡udikovich 19282009
Gokhberg, Yiśraʾel
Gokhberg, Yiśraʾel 1928
Gokhberg, Yiśraʾel 19282009
Gwkberg, Yiśraʾel
Gwkberg Yiśraʾel 19282009
Israel Gohberg Israeli mathematician
Israel Gohberg israelischer Mathematiker
Israel Gohberg matemàtic rus
Israel Gohberg matematician rus
Israel Gohberg matemático ruso
Israel Gohberg mathématicien russe
Israel Gohberg Russian mathematician
Israel Gohberg Russisch wiskundige (19282009)
Гохберг И.Ц.
Гохберг И. Ц. 19282009
Гохберг Израиль Цудикович
Гохберг Израиль Цудикович 19282009
Гохберг Ізраїль Цудикович
גוכברג, ישראל
גוכברג ישראל 19282009
ישראל גוכברג
ישראל גוכברג מתמטיקאי רוסי
イスラエル・ゴーベルグ
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