Holden, H. (Helge) 1956
Overview
Works:  101 works in 382 publications in 3 languages and 7,507 library holdings 

Genres:  Conference papers and proceedings History 
Roles:  Author, Editor, Honoree, csn, Creator, Other, Censor, Contributor, ed 
Publication Timeline
.
Most widely held works by
H Holden
Soliton equations and their algebrogeometric solutions by
Fritz Gesztesy(
)
18 editions published between 2003 and 2008 in English and held by 1,167 WorldCat member libraries worldwide
The focus of this book is on algebrogeometric solutions of completely integrable nonlinear partial differential equations in (1+1)dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sineGordon, and CamassaHolm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebrogeometric solutions in the stationary as well as timedependent contexts is provided. The formalism presented includes trace formulas, Dubrovintype initial value problems, BakerAkhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and selfcontained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exhaustive bibliography enhance the presentation offered in the main text
18 editions published between 2003 and 2008 in English and held by 1,167 WorldCat member libraries worldwide
The focus of this book is on algebrogeometric solutions of completely integrable nonlinear partial differential equations in (1+1)dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sineGordon, and CamassaHolm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebrogeometric solutions in the stationary as well as timedependent contexts is provided. The formalism presented includes trace formulas, Dubrovintype initial value problems, BakerAkhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and selfcontained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exhaustive bibliography enhance the presentation offered in the main text
The collected works of Lars Onsager : with commentary by
Lars Onsager(
)
16 editions published between 1996 and 1998 in English and held by 854 WorldCat member libraries worldwide
This volume contains the collected works of the eminent chemist and physicist Lars Onsager, one of the most influential scientists of the 20th century. The volume includes Onsager's previously unpublished PhD thesis, a biography by H.C. LonguetHiggins and M.E. Fisher, an autobiographical commentary, selected photographs, and a list of Onsager discussion remarks in print. Onsager's scientific achievements were characterized by deep insights into the natural sciences. His two bestknown accomplishments are his reciprocal relations for irreversible processes, for which he received the 1968 Nobel Prize in Chemistry, and his explicit solution of the twodimensional Ising model, a mathematical tour de force that created a sensation when it appeared. In addition, he made significant theoretical contributions to other fields, including electrolytes, colloids, superconductivity, turbulence, ice, electrons in metals, and dielectrics. In this volume, Onsager's contributions are divided into the following fields: irreversible processes; the Ising model; electrolytes; colloids; helium II and vortex quantization; offdiagonal longrange order and flux quantization; electrons in metal; turbulence; ion recombination; fluctuation theory; dielectrics; ice and water; biology; Mathieu functions. The different fields are evaluated by leading experts. The commentators are P.W. Anderson, R. Askey, A. Chorin, C. Domb, R.J. Donnelly, W. Ebeling, JC Justice, H.N.W. Lekkerkerker, P. Mazur, H.P. McKean, J.F. Nagle, T. Odijk, A.B. Pippard, G. Stell, G.H. Weiss, and C.N. Yang
16 editions published between 1996 and 1998 in English and held by 854 WorldCat member libraries worldwide
This volume contains the collected works of the eminent chemist and physicist Lars Onsager, one of the most influential scientists of the 20th century. The volume includes Onsager's previously unpublished PhD thesis, a biography by H.C. LonguetHiggins and M.E. Fisher, an autobiographical commentary, selected photographs, and a list of Onsager discussion remarks in print. Onsager's scientific achievements were characterized by deep insights into the natural sciences. His two bestknown accomplishments are his reciprocal relations for irreversible processes, for which he received the 1968 Nobel Prize in Chemistry, and his explicit solution of the twodimensional Ising model, a mathematical tour de force that created a sensation when it appeared. In addition, he made significant theoretical contributions to other fields, including electrolytes, colloids, superconductivity, turbulence, ice, electrons in metals, and dielectrics. In this volume, Onsager's contributions are divided into the following fields: irreversible processes; the Ising model; electrolytes; colloids; helium II and vortex quantization; offdiagonal longrange order and flux quantization; electrons in metal; turbulence; ion recombination; fluctuation theory; dielectrics; ice and water; biology; Mathieu functions. The different fields are evaluated by leading experts. The commentators are P.W. Anderson, R. Askey, A. Chorin, C. Domb, R.J. Donnelly, W. Ebeling, JC Justice, H.N.W. Lekkerkerker, P. Mazur, H.P. McKean, J.F. Nagle, T. Odijk, A.B. Pippard, G. Stell, G.H. Weiss, and C.N. Yang
Front tracking for hyperbolic conservation laws by
H Holden(
)
27 editions published between 2002 and 2015 in English and German and held by 595 WorldCat member libraries worldwide
This is the second edition of a wellreceived book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions, and the detailed solution of the Riemann problem for the Euler equations. Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a selfcontained presentation using front tracking, which is also a numerical℗ℓmethod. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews of the first edition: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet℗ℓ "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a onesemester graduate course." S. Noelle, Book review, German Math.℗ℓSoc. "Making it an ideal first book for the theory of nonlinear partial differential equations ... an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm
27 editions published between 2002 and 2015 in English and German and held by 595 WorldCat member libraries worldwide
This is the second edition of a wellreceived book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions, and the detailed solution of the Riemann problem for the Euler equations. Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a selfcontained presentation using front tracking, which is also a numerical℗ℓmethod. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews of the first edition: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet℗ℓ "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a onesemester graduate course." S. Noelle, Book review, German Math.℗ℓSoc. "Making it an ideal first book for the theory of nonlinear partial differential equations ... an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm
Stochastic partial differential equations : a modeling, white noise functional approach by
H Holden(
)
19 editions published in 2010 in English and held by 496 WorldCat member libraries worldwide
"The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by spacetime Brownian motion noise. In this, the second edition, the authors extend the theory to include SPDEs driven by spacetime Levy process noise, and introduce new applications of the field." "Because the authors allow the noise to be in both space and time, the solutions to SPDEs are usually of the distribution type, rather than a classical random field. To make this study rigorous and as general as possible, the discussion of SPDEs is therefore placed in the context of Hida white noise theory. The key connection between white noise theory and SPDEs is that integration with respect to Brownian random fields can be expressed as integration with respect to the Lebesgue measure of the Wick product of the integrand with Brownian white noise, and similarly with Levy processes." "Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter"Jacket
19 editions published in 2010 in English and held by 496 WorldCat member libraries worldwide
"The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by spacetime Brownian motion noise. In this, the second edition, the authors extend the theory to include SPDEs driven by spacetime Levy process noise, and introduce new applications of the field." "Because the authors allow the noise to be in both space and time, the solutions to SPDEs are usually of the distribution type, rather than a classical random field. To make this study rigorous and as general as possible, the discussion of SPDEs is therefore placed in the context of Hida white noise theory. The key connection between white noise theory and SPDEs is that integration with respect to Brownian random fields can be expressed as integration with respect to the Lebesgue measure of the Wick product of the integrand with Brownian white noise, and similarly with Levy processes." "Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter"Jacket
The Abel Prize : 20032007 : the first five years by
H Holden(
)
16 editions published between 2009 and 2010 in English and held by 458 WorldCat member libraries worldwide
The book presents the winners of the first five Abel Prizes in mathematics: 2003 JeanPierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize
16 editions published between 2009 and 2010 in English and held by 458 WorldCat member libraries worldwide
The book presents the winners of the first five Abel Prizes in mathematics: 2003 JeanPierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize
Nonlinear partial differential equations : the Abel Symposium 2010 by
H Holden(
)
20 editions published between 2012 and 2014 in English and Undetermined and held by 457 WorldCat member libraries worldwide
L.Ambrosio: Convergence of Wigner transforms in a semiclassical limit  A.Bressan: Contractive Metrics for Nonsmooth Evolutions  L. Caffarelli: Non local diffusions, drifts and games  G.Q.Chen and Y.G.Wang: Characteristic Discontinuities and Free Boundary Problems for Hyperbolic Conservation Laws  S.Conti, C.De Lellis, L.Székelyhidi Jr.: hprinciple and rigidity for C1;a isometric embeddings. J.Dolbeault, M.J.Esteban: About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities  E.Feireisl, M.E. Schonbek: On the Oberbeck–Boussinesq approximation on unbounded domains  C.Kenig: Universal Profiles and Rigidity Theorems for the Energy Critical Wave Equation  A.Kiselev, F.Nazarov: A simple energy pump for the surface quasigeostrophic equation  S.Klainerman: On the formation of trapped surfaces  R.V.Kohn: Surface Relaxation Below the Roughening Temperature: Some Recent Progress and Open Questions  A.J.Majda: Clima
20 editions published between 2012 and 2014 in English and Undetermined and held by 457 WorldCat member libraries worldwide
L.Ambrosio: Convergence of Wigner transforms in a semiclassical limit  A.Bressan: Contractive Metrics for Nonsmooth Evolutions  L. Caffarelli: Non local diffusions, drifts and games  G.Q.Chen and Y.G.Wang: Characteristic Discontinuities and Free Boundary Problems for Hyperbolic Conservation Laws  S.Conti, C.De Lellis, L.Székelyhidi Jr.: hprinciple and rigidity for C1;a isometric embeddings. J.Dolbeault, M.J.Esteban: About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities  E.Feireisl, M.E. Schonbek: On the Oberbeck–Boussinesq approximation on unbounded domains  C.Kenig: Universal Profiles and Rigidity Theorems for the Energy Critical Wave Equation  A.Kiselev, F.Nazarov: A simple energy pump for the surface quasigeostrophic equation  S.Klainerman: On the formation of trapped surfaces  R.V.Kohn: Surface Relaxation Below the Roughening Temperature: Some Recent Progress and Open Questions  A.J.Majda: Clima
Schrödinger operators : proceedings of the Nordic Summer School in Mathematics held at Sandbjerg Slot, Sønderborg, Denmark,
August 112, 1988 by
H Holden(
Book
)
21 editions published between 1989 and 2013 in English and Multiple languages and held by 435 WorldCat member libraries worldwide
Understanding quantum mechanics inevitably leads to an indepth study of the Schrdinger operator. This set of review lectures informs researchers and advanced students of the most recent developments in the analysis of the Schrdinger operator occurring in solidstate physics, nuclear physics, etc. The topics covered are nonlinear and random potentials, magnetic fields, and manybody problems. Inverse spectral theory is also treated. The results are mathematically rigorous and many physical implications are discussed. The book is suitable for advanced courses in mathematical physics
21 editions published between 1989 and 2013 in English and Multiple languages and held by 435 WorldCat member libraries worldwide
Understanding quantum mechanics inevitably leads to an indepth study of the Schrdinger operator. This set of review lectures informs researchers and advanced students of the most recent developments in the analysis of the Schrdinger operator occurring in solidstate physics, nuclear physics, etc. The topics covered are nonlinear and random potentials, magnetic fields, and manybody problems. Inverse spectral theory is also treated. The results are mathematically rigorous and many physical implications are discussed. The book is suitable for advanced courses in mathematical physics
Front tracking for hyperbolic conservation laws by
H Holden(
)
16 editions published between 2002 and 2017 in English and held by 402 WorldCat member libraries worldwide
Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a selfcontained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a onesemester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations ... an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm
16 editions published between 2002 and 2017 in English and held by 402 WorldCat member libraries worldwide
Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a selfcontained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a onesemester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations ... an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm
The Abel Prize 20082012 by
H Holden(
)
16 editions published between 2013 and 2014 in English and held by 395 WorldCat member libraries worldwide
Covering the years 20082012, this book profiles the life and work of recent winners of the Abel Prize: John G. Thompson and Jacques Tits  2008, Mikhail Gromov  2009, John T. Tate Jr.  2010, John W. Milnor  2011, Endre Szemeredi  2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos  old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/).The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau.This book follows on The Abel Prize: 20032007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners
16 editions published between 2013 and 2014 in English and held by 395 WorldCat member libraries worldwide
Covering the years 20082012, this book profiles the life and work of recent winners of the Abel Prize: John G. Thompson and Jacques Tits  2008, Mikhail Gromov  2009, John T. Tate Jr.  2010, John W. Milnor  2011, Endre Szemeredi  2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos  old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/).The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau.This book follows on The Abel Prize: 20032007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners
Hyperbolic conservation laws and related analysis with applications : Edinburgh, September 2011 by
GuiQiang Chen(
)
12 editions published between 2013 and 2016 in English and held by 393 WorldCat member libraries worldwide
This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation. Also included are articles on recent advances in the Euler equations and the NavierStokesFourierPoisson system, in addition to new results on collective phenomena described by the CuckerSmale model. The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume. It is addressed to researchers and graduate students interested in partial differential equations and related analysis with applications
12 editions published between 2013 and 2016 in English and held by 393 WorldCat member libraries worldwide
This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation. Also included are articles on recent advances in the Euler equations and the NavierStokesFourierPoisson system, in addition to new results on collective phenomena described by the CuckerSmale model. The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume. It is addressed to researchers and graduate students interested in partial differential equations and related analysis with applications
Stochastic partial differential equations : a modeling, white noise functional approach by
H Holden(
Book
)
17 editions published in 1996 in English and held by 368 WorldCat member libraries worldwide
This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in reservoir theory and related areas. 3) The theory should be strong and efficient enough to allow us to solve th, ~se SPDEs explicitly, or at least provide algorithms or approximations for the solutions
17 editions published in 1996 in English and held by 368 WorldCat member libraries worldwide
This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in reservoir theory and related areas. 3) The theory should be strong and efficient enough to allow us to solve th, ~se SPDEs explicitly, or at least provide algorithms or approximations for the solutions
Soliton equations and their algebrogeometric solutions by
Fritz Gesztesy(
)
4 editions published in 2008 in English and held by 360 WorldCat member libraries worldwide
Detailed treatment of the class of algebrogeometric solutions and their representations in terms of Riemann theta functions
4 editions published in 2008 in English and held by 360 WorldCat member libraries worldwide
Detailed treatment of the class of algebrogeometric solutions and their representations in terms of Riemann theta functions
Spectral analysis, differential equations, and mathematical physics : a festschrift in honor of Fritz Gesztesy's 60th birthday by
H Holden(
Book
)
13 editions published between 2013 and 2014 in English and held by 256 WorldCat member libraries worldwide
13 editions published between 2013 and 2014 in English and held by 256 WorldCat member libraries worldwide
Nonlinear partial differential equations and hyperbolic wave phenomena : 20082009 Research Program on Nonlinear Partial Differential
Equations, Centre for Advanced Study of the Norwegian Academy of Sciences and Letters, Oslo, Norway by
Norske videnskapsakademi(
Book
)
17 editions published between 2010 and 2012 in English and held by 246 WorldCat member libraries worldwide
This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 200809
17 editions published between 2010 and 2012 in English and held by 246 WorldCat member libraries worldwide
This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 200809
Splitting methods for partial differential equations with rough solutions : analysis and MATLAB programs by
H Holden(
Book
)
10 editions published in 2010 in English and held by 157 WorldCat member libraries worldwide
Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convectiondiffusion equations. Common for these equations is the prevalence of rough, or nonsmooth, solutions, e.g., shocks
10 editions published in 2010 in English and held by 157 WorldCat member libraries worldwide
Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convectiondiffusion equations. Common for these equations is the prevalence of rough, or nonsmooth, solutions, e.g., shocks
Solvable models in quantum mechanics by
Sergio Albeverio(
)
4 editions published between 1988 and 2014 in English and held by 68 WorldCat member libraries worldwide
"This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided. The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around twobody point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around twobody point interaction problems, is followed by a bibliography focusing on essential developments made since 1988."Résumé de l'éditeur
4 editions published between 1988 and 2014 in English and held by 68 WorldCat member libraries worldwide
"This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided. The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around twobody point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around twobody point interaction problems, is followed by a bibliography focusing on essential developments made since 1988."Résumé de l'éditeur
Nonlinear partial differential equations, mathematical physics, and stochastic analysis : the Helge Holden anniversary volume by Mathematical Physics and Stochastic Analysis Nonlinear PDEs(
Book
)
3 editions published in 2018 in English and held by 28 WorldCat member libraries worldwide
This volume is dedicated to Helge Holden on the occasion of his 60th anniversary. It collects contributions by numerous scientists with expertise in nonlinear partial differential equations (PDEs), mathematical physics, and stochastic analysis, reflecting to a large degree Helge Holden's longstanding research interests. Accordingly, the problems addressed in the contributions deal with a large range of topics, including, in particular, infinitedimensional analysis, linear and nonlinear PDEs, stochastic analysis, spectral theory, completely integrable systems, random matrix theory, and chaotic dynamics and sestina poetry. They represent to some extent the lectures presented at the conference Nonlinear PDEs, Mathematical Physics and Stochastic Analysis, held at NTNU, Trondheim, July 47, 2016 (https://wiki.math.ntnu.no/holden60). The mathematical tools involved draw from a wide variety of techniques in functional analysis, operator theory, and probability theory. This collection of research papers will be of interest to any active scientist working in one of the above mentioned areas
3 editions published in 2018 in English and held by 28 WorldCat member libraries worldwide
This volume is dedicated to Helge Holden on the occasion of his 60th anniversary. It collects contributions by numerous scientists with expertise in nonlinear partial differential equations (PDEs), mathematical physics, and stochastic analysis, reflecting to a large degree Helge Holden's longstanding research interests. Accordingly, the problems addressed in the contributions deal with a large range of topics, including, in particular, infinitedimensional analysis, linear and nonlinear PDEs, stochastic analysis, spectral theory, completely integrable systems, random matrix theory, and chaotic dynamics and sestina poetry. They represent to some extent the lectures presented at the conference Nonlinear PDEs, Mathematical Physics and Stochastic Analysis, held at NTNU, Trondheim, July 47, 2016 (https://wiki.math.ntnu.no/holden60). The mathematical tools involved draw from a wide variety of techniques in functional analysis, operator theory, and probability theory. This collection of research papers will be of interest to any active scientist working in one of the above mentioned areas
The Abel prize 20032007 ; the first five years by
H Holden(
)
3 editions published in 2010 in English and held by 27 WorldCat member libraries worldwide
3 editions published in 2010 in English and held by 27 WorldCat member libraries worldwide
Stochastic Partial Differential Equations : a Modeling, White Noise Functional Approach by
H Holden(
)
5 editions published in 2010 in English and held by 27 WorldCat member libraries worldwide
The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by spacetime Brownian motion noise. In this, the second edition, the authors extend the theory to include SPDEs driven by spacetime Lévy process noise, and introduce new applications of the field. Because the authors allow the noise to be in both space and time, the solutions to SPDEs are usually of the distribution type, rather than a classical random field. To make this study rigorous and as general as possible, the discussion of SPDEs is therefore placed in the context of Hida white noise theory. The key connection between white noise theory and SPDEs is that integration with respect to Brownian random fields can be expressed as integration with respect to the Lebesgue measure of the Wick product of the integrand with Brownian white noise, and similarly with Lévy processes. The first part of the book deals with the classical Brownian motion case. The second extends it to the Lévy white noise case. For SPDEs of the Wick type, a general solution method is given by means of the Hermite transform, which turns a given SPDE into a parameterized family of deterministic PDEs. Applications of this theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter. From the reviews of the first edition: "The authors have made significant contributions to each of the areas. As a whole, the book is well organized and very carefully written and the details of the proofs are basically spelled out... This is a rich and demanding book... It will be of great value for students of probability theory or SPDEs with an interest in the subject, and also for professional probabilists." Mathematical Reviews "...a comprehensive introduction to stochastic partial differential equations." Zentralblatt MATH
5 editions published in 2010 in English and held by 27 WorldCat member libraries worldwide
The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by spacetime Brownian motion noise. In this, the second edition, the authors extend the theory to include SPDEs driven by spacetime Lévy process noise, and introduce new applications of the field. Because the authors allow the noise to be in both space and time, the solutions to SPDEs are usually of the distribution type, rather than a classical random field. To make this study rigorous and as general as possible, the discussion of SPDEs is therefore placed in the context of Hida white noise theory. The key connection between white noise theory and SPDEs is that integration with respect to Brownian random fields can be expressed as integration with respect to the Lebesgue measure of the Wick product of the integrand with Brownian white noise, and similarly with Lévy processes. The first part of the book deals with the classical Brownian motion case. The second extends it to the Lévy white noise case. For SPDEs of the Wick type, a general solution method is given by means of the Hermite transform, which turns a given SPDE into a parameterized family of deterministic PDEs. Applications of this theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter. From the reviews of the first edition: "The authors have made significant contributions to each of the areas. As a whole, the book is well organized and very carefully written and the details of the proofs are basically spelled out... This is a rich and demanding book... It will be of great value for students of probability theory or SPDEs with an interest in the subject, and also for professional probabilists." Mathematical Reviews "...a comprehensive introduction to stochastic partial differential equations." Zentralblatt MATH
Local conservation laws and the Hamiltonian formalism for the Toda hierarchy revisited by
Fritz Gesztesy(
Book
)
4 editions published in 2006 in English and held by 21 WorldCat member libraries worldwide
4 editions published in 2006 in English and held by 21 WorldCat member libraries worldwide
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 Gesztesy, Fritz 1953 Contributor Honoree Dedicatee Author Editor
 Risebro, Nils Henrik Other Editor
 Karlsen, Kenneth Hvistendahl Other Author Editor
 Piene, Ragni Other Contributor Editor
 Kjelstrup, Signe Other Editor
 Hemmer, P. C. (Per Christian) 1933 Other Author Editor
 Onsager, Lars 19031976 Author
 Teschl, Gerald Editor
 Jensen, A. (Arne) 1950 Editor
 Chen, GuiQiang 1963 Author Editor
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Chemistry, Physical and theoretical Computer science Conservation laws (Mathematics) Differential equations Differential equations, Hyperbolic Differential equations, Nonlinear Differential equations, NonlinearNumerical solutions Differential equations, Partial Distribution (Probability theory) Engineering mathematics Global analysis (Mathematics) History Mathematical analysis Mathematical models Mathematical physics Mathematics MathematicsAwards Mine accidents Miners Nonlinear partial differential operators Numerical analysis Onsager, Lars, Physics Probabilities Quantum computing Quantum theory Quantum theoryMathematical models Queensland QueenslandMount Isa Region Schrödinger operator Solitons Stochastic analysis Stochastic partial differential equations
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Helge Holden matemático noruego
Helge Holden matematico norvegese
Helge Holden Noors wiskundige
Helge Holden norsk professor och matematiker
Helge Holden norsk professor og matematikar
Helge Holden norsk professor og matematiker
Helge Holden Norwegian mathematician
Helge Holden norwegischer Mathematiker
Holden, H.
Holden, H. 1956
Holden, H. (Helge), 1956
Holden, Helge
Holden, Helge 1956
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