Nikolʹskiĭ, N. K. (Nikolaĭ Kapitonovich)
Overview
Works:  114 works in 381 publications in 3 languages and 5,701 library holdings 

Genres:  Conference proceedings History 
Roles:  Author, Editor, Publishing director, Thesis advisor, ed 
Classifications:  QA403, 515.2433 
Publication Timeline
.
Most widely held works by
N. K Nikolʹskiĭ
Treatise on the shift operator : spectral function theory by
N. K Nikolʹskiĭ(
Book
)
28 editions published between 1980 and 2012 in English and Russian and held by 450 WorldCat member libraries worldwide
28 editions published between 1980 and 2012 in English and Russian and held by 450 WorldCat member libraries worldwide
Functional analysis I : linear functional analysis by
I︠U︡. I Li︠u︡bich(
Book
)
16 editions published between 1991 and 1992 in English and held by 331 WorldCat member libraries worldwide
The twentieth century view of the analysis of functions is dominated by the study of classes of functions, as contrasted with the older emphasis on the study of individual functions. Operator theory has had a similar evolution, leading to a primary role for families of operators. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach. The book consists of two chapters, the first of which deals with classical aspects of the subject, while the second presents the abstract modern theory and some of its applications. Both chapters are divided into sections which are devoted to individual topics. For each topic the origins are traced, the principal definitions and results are stated and illustrative examples for theory and applications are given. Usually proofs are omitted, although certain sections of Chapter 2 do contain some quite detailed proofs. The classical concrete problems of Chapter 1 provide motivation and examples, as well as a technical foundation, for the theory in Chapter 2
16 editions published between 1991 and 1992 in English and held by 331 WorldCat member libraries worldwide
The twentieth century view of the analysis of functions is dominated by the study of classes of functions, as contrasted with the older emphasis on the study of individual functions. Operator theory has had a similar evolution, leading to a primary role for families of operators. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach. The book consists of two chapters, the first of which deals with classical aspects of the subject, while the second presents the abstract modern theory and some of its applications. Both chapters are divided into sections which are devoted to individual topics. For each topic the origins are traced, the principal definitions and results are stated and illustrative examples for theory and applications are given. Usually proofs are omitted, although certain sections of Chapter 2 do contain some quite detailed proofs. The classical concrete problems of Chapter 1 provide motivation and examples, as well as a technical foundation, for the theory in Chapter 2
Complex analysis and spectral theory seminar : Leningrad 197980 by
Viktor Petrovich Khavin(
Book
)
11 editions published in 1981 in English and held by 323 WorldCat member libraries worldwide
11 editions published in 1981 in English and held by 323 WorldCat member libraries worldwide
Commutative harmonic analysis I : general survey, classical aspects by
Viktor Petrovich Khavin(
Book
)
20 editions published between 1989 and 2011 in English and held by 320 WorldCat member libraries worldwide
This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numer rous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a "miniZygmund" for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail. There is also a thorough introduction to CalderonZygmund theory
20 editions published between 1989 and 2011 in English and held by 320 WorldCat member libraries worldwide
This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numer rous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a "miniZygmund" for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail. There is also a thorough introduction to CalderonZygmund theory
Operators, functions, and systems : an easy reading by
N. K Nikolʹskiĭ(
Book
)
13 editions published in 2002 in English and held by 312 WorldCat member libraries worldwide
13 editions published in 2002 in English and held by 312 WorldCat member libraries worldwide
Linear and complex analysis problem book 3 by
Viktor Petrovich Khavin(
Book
)
15 editions published in 1994 in English and held by 290 WorldCat member libraries worldwide
Presents a collection of unsolved problems of modern analysis designed as informally written miniarticles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references
15 editions published in 1994 in English and held by 290 WorldCat member libraries worldwide
Presents a collection of unsolved problems of modern analysis designed as informally written miniarticles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references
Commutative harmonic analysis IV : harmonic analysis in IRn by
Viktor Petrovich Khavin(
Book
)
13 editions published between 1991 and 1992 in English and held by 230 WorldCat member libraries worldwide
With the groundwork laid in the first volume (EMS 15) of the Commutative Harmonic Analysis subseries of the Encyclopaedia, the present volume takes up four advanced topics in the subject: LittlewoodPaley theory for singular integrals, exceptional sets, multiple Fourier series and multiple Fourier integrals. The authors assume that the reader is familiar with the fundamentals of harmonic analysis and with basic functional analysis. The exposition starts with the basics for each topic, also taking account of the historical development, and ends by bringing the subject to the level of current research. Table of Contents I. Multiple Fourier Series and Fourier Integrals. Sh. A. Alimov, R.R. Ashurov, A.K. Pulatov II. Methods of the Theory of Singular Integrals. II: Littlewood Paley Theory and its Applications E.M. Dyn'kin III. Exceptional Sets in Harmonic Analysis S.V. Kislyakov
13 editions published between 1991 and 1992 in English and held by 230 WorldCat member libraries worldwide
With the groundwork laid in the first volume (EMS 15) of the Commutative Harmonic Analysis subseries of the Encyclopaedia, the present volume takes up four advanced topics in the subject: LittlewoodPaley theory for singular integrals, exceptional sets, multiple Fourier series and multiple Fourier integrals. The authors assume that the reader is familiar with the fundamentals of harmonic analysis and with basic functional analysis. The exposition starts with the basics for each topic, also taking account of the historical development, and ends by bringing the subject to the level of current research. Table of Contents I. Multiple Fourier Series and Fourier Integrals. Sh. A. Alimov, R.R. Ashurov, A.K. Pulatov II. Methods of the Theory of Singular Integrals. II: Littlewood Paley Theory and its Applications E.M. Dyn'kin III. Exceptional Sets in Harmonic Analysis S.V. Kislyakov
Complex analysis I : entire and meromorphic functions, polyanalytic functions and their generalizations by
A. A Golʹdberg(
Book
)
10 editions published between 1996 and 2010 in English and held by 223 WorldCat member libraries worldwide
The first part of the volume contains a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications. It includes the fundamental notions, methods and results on the growth of entire functions and the distribution of their zeros, the Rolf Nevanlinna theory of distribution of values of meromorphic functions including the inverse problem, the theory of completely regular growth, the concept of limit sets for entire and subharmonic functions. The authors describe the interpolation by entire functions, to entire and meromorphic solutions of ordinary differential equations, to the Riemann boundary problem with an infinite index and to the arithmetic of the convolution semigroup of probability distributions. Polyanalytic functions form one of the most natural generalizations of analytic functions and are described in Part II. They emerged for the first time in plane elasticity theory where they found important applications (due to Kolossof, Mushelishvili etc.). This book contains a detailed review of recent investigations concerning the functiontheoretical pecularities of polyanalytic functions (boundary behavour, value distributions, degeneration, uniqueness etc.). Polyanalytic functions have many points of contact with such fields of analysis as polyharmonic functions, Nevanlinna Theory, meromorphic curves, cluster set theory, functions of several complex variables etc
10 editions published between 1996 and 2010 in English and held by 223 WorldCat member libraries worldwide
The first part of the volume contains a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications. It includes the fundamental notions, methods and results on the growth of entire functions and the distribution of their zeros, the Rolf Nevanlinna theory of distribution of values of meromorphic functions including the inverse problem, the theory of completely regular growth, the concept of limit sets for entire and subharmonic functions. The authors describe the interpolation by entire functions, to entire and meromorphic solutions of ordinary differential equations, to the Riemann boundary problem with an infinite index and to the arithmetic of the convolution semigroup of probability distributions. Polyanalytic functions form one of the most natural generalizations of analytic functions and are described in Part II. They emerged for the first time in plane elasticity theory where they found important applications (due to Kolossof, Mushelishvili etc.). This book contains a detailed review of recent investigations concerning the functiontheoretical pecularities of polyanalytic functions (boundary behavour, value distributions, degeneration, uniqueness etc.). Polyanalytic functions have many points of contact with such fields of analysis as polyharmonic functions, Nevanlinna Theory, meromorphic curves, cluster set theory, functions of several complex variables etc
Kolmogorov's heritage in mathematics by
Éric Charpentier(
Book
)
17 editions published between 2004 and 2007 in English and French and held by 219 WorldCat member libraries worldwide
A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by K
17 editions published between 2004 and 2007 in English and French and held by 219 WorldCat member libraries worldwide
A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by K
Selected problems of weighted approximation and spectral analysis by
N. K Nikolʹskiĭ(
Book
)
8 editions published between 1974 and 1976 in English and Russian and held by 200 WorldCat member libraries worldwide
8 editions published between 1974 and 1976 in English and Russian and held by 200 WorldCat member libraries worldwide
Commutative harmonic analysis III : generalized functions, applications by
Viktor Petrovich Khavin(
Book
)
13 editions published in 1995 in English and held by 197 WorldCat member libraries worldwide
This EMS volume shows the great power provided by modern harmonic analysis, not only in mathematics, but also in mathematical physics and engineering. Aimed at a reader who has learned the principles of harmonic analysis, this book is intended to provide a variety of perspectives on this important classical subject. The authors have written an outstanding book which distinguishes itself by the authors' excellent expository style. It can be useful for the expert in one area of harmonic analysis who wishes to obtain broader knowledge of other aspects of the subject and also by graduate students in other areas of mathematics who wish a general but rigorous introduction to the subject
13 editions published in 1995 in English and held by 197 WorldCat member libraries worldwide
This EMS volume shows the great power provided by modern harmonic analysis, not only in mathematics, but also in mathematical physics and engineering. Aimed at a reader who has learned the principles of harmonic analysis, this book is intended to provide a variety of perspectives on this important classical subject. The authors have written an outstanding book which distinguishes itself by the authors' excellent expository style. It can be useful for the expert in one area of harmonic analysis who wishes to obtain broader knowledge of other aspects of the subject and also by graduate students in other areas of mathematics who wish a general but rigorous introduction to the subject
Investigations in linear operators and function theory by
N. K Nikolʹskiĭ(
Book
)
7 editions published between 1972 and 1995 in English and Russian and held by 193 WorldCat member libraries worldwide
7 editions published between 1972 and 1995 in English and Russian and held by 193 WorldCat member libraries worldwide
Commutative harmonic analysis II : group methods in commutative harmonic analysis by
Viktor Petrovich Khavin(
Book
)
11 editions published between 1991 and 1998 in English and held by 185 WorldCat member libraries worldwide
Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop (and still does), conquering new unexpected areas and producing impressive applications to a multitude of problems, old and new, ranging from arithmetic to optics, from geometry to quantum mechanics, not to mention analysis and differential equations. The power of group theoretic ideology is successfully illustrated by this wide range of topics. It is widely understood now that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This volume is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in the present volume can hardly be found in any monograph. This book will be very useful to a wide circle of readers, including mathematicians, theoretical physicists and engineers
11 editions published between 1991 and 1998 in English and held by 185 WorldCat member libraries worldwide
Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop (and still does), conquering new unexpected areas and producing impressive applications to a multitude of problems, old and new, ranging from arithmetic to optics, from geometry to quantum mechanics, not to mention analysis and differential equations. The power of group theoretic ideology is successfully illustrated by this wide range of topics. It is widely understood now that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This volume is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in the present volume can hardly be found in any monograph. This book will be very useful to a wide circle of readers, including mathematicians, theoretical physicists and engineers
Toeplitz operators and spectral function theory : essays from the Leningrad Seminar on Operator Theory by
N. K Nikolʹskiĭ(
Book
)
10 editions published in 1989 in English and held by 179 WorldCat member libraries worldwide
10 editions published in 1989 in English and held by 179 WorldCat member libraries worldwide
Complex analysis, operators, and related topics : the S.A. Vinogradov memorial volume(
Book
)
7 editions published in 2000 in English and held by 164 WorldCat member libraries worldwide
This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. It consists of 30 carefully selected surveys and research papers. The main subjects of the volume include: free interpolation by analytic functions in its development from the pathbreaking works by L. Carleson up to the most recent achievements and in its connections with the theory of singular integral operators and Carlesontype embedding theorems, moment problems etc. SzkefalviNagyFoias model spaces studied from the point of view of holomorphic spaces holomorphic spaces (Hardy, Bergman, Hlder, and Sobolev spaces) analytic functions smooth up to the boundary with their subtle properties related to the NevanlinnaSmirnov factorization, division and multiplication, and zero sets a new approach to weighted inequalities for singular integrals based on the Bellman function in optimization theory; the uncertainty principle in harmonic analysis and, in particular, a complete version of Turans lemma on trigonometric sums Hankel operators and stationary Gaussian processes Fourier multipliers, and spectral analysis of some differential operators. These themes are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques. The book is dedicated to the memory of S.A. Vinogradov. It contains a bibliographical note (with a lively portrait) of S.A. Vinogradov, a detailed survey of his mathematical achievements, and a complete list of publications, as well as the translations of two of Vinogradovs surveys whose Russian originals are now hardly accessible
7 editions published in 2000 in English and held by 164 WorldCat member libraries worldwide
This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. It consists of 30 carefully selected surveys and research papers. The main subjects of the volume include: free interpolation by analytic functions in its development from the pathbreaking works by L. Carleson up to the most recent achievements and in its connections with the theory of singular integral operators and Carlesontype embedding theorems, moment problems etc. SzkefalviNagyFoias model spaces studied from the point of view of holomorphic spaces holomorphic spaces (Hardy, Bergman, Hlder, and Sobolev spaces) analytic functions smooth up to the boundary with their subtle properties related to the NevanlinnaSmirnov factorization, division and multiplication, and zero sets a new approach to weighted inequalities for singular integrals based on the Bellman function in optimization theory; the uncertainty principle in harmonic analysis and, in particular, a complete version of Turans lemma on trigonometric sums Hankel operators and stationary Gaussian processes Fourier multipliers, and spectral analysis of some differential operators. These themes are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques. The book is dedicated to the memory of S.A. Vinogradov. It contains a bibliographical note (with a lively portrait) of S.A. Vinogradov, a detailed survey of his mathematical achievements, and a complete list of publications, as well as the translations of two of Vinogradovs surveys whose Russian originals are now hardly accessible
Systems, approximation, singular integral operators, and related topics : International Workshop on Operator Theory and Applications,
IWOTA 2000 by
Alexander A Borichev(
Book
)
6 editions published in 2001 in English and held by 93 WorldCat member libraries worldwide
This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include:  spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers;  multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations;  Hankel operators and forms;  operator algebras;  the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations;  approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques
6 editions published in 2001 in English and held by 93 WorldCat member libraries worldwide
This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include:  spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers;  multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations;  Hankel operators and forms;  operator algebras;  the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations;  approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques
Leçons de mathématiques d'aujourd'hui(
Book
)
2 editions published in 2003 in French and held by 89 WorldCat member libraries worldwide
2 editions published in 2003 in French and held by 89 WorldCat member libraries worldwide
Leçons de mathématiques d'aujourd'hui by
JeanPierre Kahane(
Book
)
5 editions published between 2000 and 2003 in French and held by 88 WorldCat member libraries worldwide
5 editions published between 2000 and 2003 in French and held by 88 WorldCat member libraries worldwide
Leçons de mathématiques d'aujourd'hui(
Book
)
4 editions published between 2003 and 2012 in French and held by 84 WorldCat member libraries worldwide
4 editions published between 2003 and 2012 in French and held by 84 WorldCat member libraries worldwide
Leçons de mathématiques d'aujourd'hui by
B Perthame(
Book
)
3 editions published in 2007 in French and held by 77 WorldCat member libraries worldwide
3 editions published in 2007 in French and held by 77 WorldCat member libraries worldwide
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Related Identities
 Khavin, Viktor Petrovich Thesis advisor Author Editor
 Charpentier, Éric Publishing director Author Editor
 Lesne, Annick Publishing director Editor
 Kolmogorov, A. N. (Andreĭ Nikolaevich) 19031987 Author
 Gonchar, A. A. (Andrei A.) Editor
 Matematicheskiĭ institut im. V.A. Steklova
 Vinogradov, S. A. (Stanislav Aleksandrovich) 19411997
 Borichev, Alexander A. 1963 Author Editor
 Kahane, JeanPierre Author
 École doctorale de Mathématiques et Informatique (Bordeaux) Editor
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Associated Subjects
Analytic functions Approximation theory Control theory Differentiable dynamical systems Distribution (Probability theory) Fourier analysis Fourier series Functional analysis Functions Functions, Entire Functions, Meromorphic Functions of complex variables Functions of several complex variables Global analysis (Mathematics) Group theory Harmonic analysis Harmonic functions Influence (Literary, artistic, etc.) Invariant subspaces Kolmogorov, A. N.(Andreĭ Nikolaevich), Kolmogorov complexity Linear operators Logic, Symbolic and mathematical Mathematical analysis Mathematics Operator theory Potential theory (Mathematics) Shift operators (Operator theory) Sidon sets Singular integrals Spectral theory (Mathematics) Toeplitz operators Topological groups Topology
Alternative Names
Nikolai Kapitonowitsch Nikolski mathmaticien russe
Nikolski, N. K.
Nikolski, N.K. 1940
Nikolski, N. K. (Nikolai K.)
Nikolski, Nicola
Nikolski Nicola 1940....
Nikolski Nicolas 1940....
Nikolski Nikola 1940....
Nikolski, Nikola K.
Nikolski, Nikolai K. 1940
Nikolʹsk, Nikola Kapitonovich
Nikolʹsk, Nikola Kapitonovich 1940...
Nikolsk, Nikola Kapitonovitch 1940...
Nikolskii, N.K.
Nikolʹskiĭ, N. K. 1940
Nikolʹskii, Nikolai K.
Nikolʹskiĭ, Nikolaĭ K. 1940
Nikolʹskiĭ, Nikolaĭ Kapitonovich
Nikolʹskiĭ, Nikolaĭ Kapitonovich 1940
Nikolʹskij, N. K.
Nikolʹskij, N. K. 1940
Nikolʹskij, N. K. (Nikolaj Kapitonovich)
Nikolʹskij, Nikolaj 1940
Nikolʹskij, Nikolaj Kapitonovič
Nikolʹskij, Nikolaj Kapitonovič 1940
Nikolʹskij, Nikolaj Kapitonovich
Nikolʹskij, Nikolaj Kapitonovich 1940
Н.К. Никольский
Никольский, Николай Капитонович
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