Simon, Barry 1946
Overview
Works:  187 works in 1,061 publications in 4 languages and 16,787 library holdings 

Genres:  Conference papers and proceedings Festschriften Academic theses 
Roles:  Author, Editor, Honoree, Other, Collector, Dedicatee, Thesis advisor, htt, Contributor 
Classifications:  QC20, 530.15 
Publication Timeline
.
Most widely held works about
Barry Simon
Most widely held works by
Barry Simon
Szegő's theorem and its descendants : spectral theory for L² perturbations of orthogonal polynomials by
Barry Simon(
)
27 editions published between 2010 and 2011 in English and held by 1,750 WorldCat member libraries worldwide
This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first booklength treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and KillipSimon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC
27 editions published between 2010 and 2011 in English and held by 1,750 WorldCat member libraries worldwide
This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first booklength treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and KillipSimon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC
Quantum mechanics for Hamiltonians defined as quadratic forms by
Barry Simon(
)
27 editions published between 1970 and 2016 in English and held by 1,459 WorldCat member libraries worldwide
"It is our purpose in this monograph to present a complete, rigorous mathematical treatment of two body quantum mechanics for a wider class of potentials than is normally treated in the literature. work: At the same time, we will review the theory of the "usual" Kato classes, although no at Ư tempt has been made to make this review exhaustive or complete. The scope of what we present is best delineated by stating the limits of this we take for granted the standard Hilbert space formalism, and our main goal is to prove forward dispersion relations from first principles. For example we do not assume the LippmanSchwinger equation but prove it within the framework of timedependent scattering theory."Introduction
27 editions published between 1970 and 2016 in English and held by 1,459 WorldCat member libraries worldwide
"It is our purpose in this monograph to present a complete, rigorous mathematical treatment of two body quantum mechanics for a wider class of potentials than is normally treated in the literature. work: At the same time, we will review the theory of the "usual" Kato classes, although no at Ư tempt has been made to make this review exhaustive or complete. The scope of what we present is best delineated by stating the limits of this we take for granted the standard Hilbert space formalism, and our main goal is to prove forward dispersion relations from first principles. For example we do not assume the LippmanSchwinger equation but prove it within the framework of timedependent scattering theory."Introduction
Methods of modern mathematical physics by
Michael Reed(
Book
)
64 editions published between 1972 and 2010 in 4 languages and held by 1,214 WorldCat member libraries worldwide
"This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially selfcontained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations." Publisher description
64 editions published between 1972 and 2010 in 4 languages and held by 1,214 WorldCat member libraries worldwide
"This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially selfcontained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations." Publisher description
The statistical mechanics of lattice gases by
Barry Simon(
)
13 editions published between 1993 and 2016 in English and held by 1,116 WorldCat member libraries worldwide
Annotation
13 editions published between 1993 and 2016 in English and held by 1,116 WorldCat member libraries worldwide
Annotation
Studies in mathematical physics : essays in honor of Valentine Bargmann by
Elliott H Lieb(
)
21 editions published in 1976 in English and Italian and held by 1,092 WorldCat member libraries worldwide
The inverse rsquared force: an introduction to its symmetries. Certain Hilbert spaces of analytic functions associated with the Heisenberg group. Lower bound for the ground state energy of the Schrodinger equation using the sharp form of young's inequality. Alternative theories of gravitation. Generalized wronskian relation: a novel approach to Bargmannequivalent and phaseequivalent potentials. Old and new approaches to the inverse scattering problem. A family of optimal conditions for the absence of bound states in a potential. Spinning tops in external fields. Measures on the finite dimensional subspaces of a Hilbert space. The Froissart bound and crossing symetry. Intertwining operators for SL. Inequalities for the moments of the Eigenvalues of the Schrodinger Hamiltonian and their relation to Sobolev inequalities. On the number of bound states of two body Schrodinger operators: a review. Quantum dynamics: from automorphism to Hamiltonian. Semiclassical analysis illuminateot of a fi19991222
21 editions published in 1976 in English and Italian and held by 1,092 WorldCat member libraries worldwide
The inverse rsquared force: an introduction to its symmetries. Certain Hilbert spaces of analytic functions associated with the Heisenberg group. Lower bound for the ground state energy of the Schrodinger equation using the sharp form of young's inequality. Alternative theories of gravitation. Generalized wronskian relation: a novel approach to Bargmannequivalent and phaseequivalent potentials. Old and new approaches to the inverse scattering problem. A family of optimal conditions for the absence of bound states in a potential. Spinning tops in external fields. Measures on the finite dimensional subspaces of a Hilbert space. The Froissart bound and crossing symetry. Intertwining operators for SL. Inequalities for the moments of the Eigenvalues of the Schrodinger Hamiltonian and their relation to Sobolev inequalities. On the number of bound states of two body Schrodinger operators: a review. Quantum dynamics: from automorphism to Hamiltonian. Semiclassical analysis illuminateot of a fi19991222
Convexity : an analytic viewpoint by
Barry Simon(
)
26 editions published between 2011 and 2015 in English and Undetermined and held by 1,021 WorldCat member libraries worldwide
"Convexity of sets and functions are extremely simple notions to define, so it may be somewhat surprising the depth and breadth of ideas that these notions give rise to. It turns out that convexity is central to a vast number of applied areas, including Statistical Mechanics, Thermodynamics, Mathematical Economics, and Statistics, and that many inequalities, including Hölder's and Minkowski's inequalities, are related to convexity. An introductory chapter (1) includes a study of regularity properties of convex functions, some inequalities (Hölder, Minkowski, and Jensen), the HahnBanach theorem as a statement about extending tangents to convex functions, and the introduction of two constructions that will play major roles later in this book: the Minkowski gauge of a convex set and the Legendre transform of a function"
26 editions published between 2011 and 2015 in English and Undetermined and held by 1,021 WorldCat member libraries worldwide
"Convexity of sets and functions are extremely simple notions to define, so it may be somewhat surprising the depth and breadth of ideas that these notions give rise to. It turns out that convexity is central to a vast number of applied areas, including Statistical Mechanics, Thermodynamics, Mathematical Economics, and Statistics, and that many inequalities, including Hölder's and Minkowski's inequalities, are related to convexity. An introductory chapter (1) includes a study of regularity properties of convex functions, some inequalities (Hölder, Minkowski, and Jensen), the HahnBanach theorem as a statement about extending tangents to convex functions, and the introduction of two constructions that will play major roles later in this book: the Minkowski gauge of a convex set and the Legendre transform of a function"
The P([Greek letter phi])₂ Euclidean (quantum) field theory by
Barry Simon(
)
18 editions published between 1974 and 1976 in 3 languages and held by 1,004 WorldCat member libraries worldwide
18 editions published between 1974 and 1976 in 3 languages and held by 1,004 WorldCat member libraries worldwide
Functional integration and quantum physics by
Barry Simon(
Book
)
8 editions published in 1979 in English and held by 590 WorldCat member libraries worldwide
The main theme of this classic book is the path integral technique and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of FeynmanKac formula. Starting with main examples of Gaussian processes, the author presents four different proofs of the FeynmanKac formula
8 editions published in 1979 in English and held by 590 WorldCat member libraries worldwide
The main theme of this classic book is the path integral technique and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of FeynmanKac formula. Starting with main examples of Gaussian processes, the author presents four different proofs of the FeynmanKac formula
Representations of finite and compact groups by
Barry Simon(
Book
)
23 editions published between 1900 and 2012 in English and held by 480 WorldCat member libraries worldwide
23 editions published between 1900 and 2012 in English and held by 480 WorldCat member libraries worldwide
Schrödinger operators, with applications to quantum mechanics and global geometry by
H. L Cycon(
Book
)
14 editions published between 1987 and 2008 in English and Russian and held by 393 WorldCat member libraries worldwide
A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quanturn mechanics. Furthermore recent research shows that it also helps to deepen our insight into global differential geometry. This monograph written for both graduate students and researchers summarizes and synthesizes the theory of Schrödinger operators emphasizing the progress made in the last decade by Lieb, Enss, Witten and others. Besides general properties, the book covers, in particular, multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory, quantum mechanics in constant electric and magnetic fields, Schrödinger operators with random and almost periodic potentials and, finally, Schrödinger operator methods in differential geometry to prove the Morse inequalities and the index theorem
14 editions published between 1987 and 2008 in English and Russian and held by 393 WorldCat member libraries worldwide
A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quanturn mechanics. Furthermore recent research shows that it also helps to deepen our insight into global differential geometry. This monograph written for both graduate students and researchers summarizes and synthesizes the theory of Schrödinger operators emphasizing the progress made in the last decade by Lieb, Enss, Witten and others. Besides general properties, the book covers, in particular, multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory, quantum mechanics in constant electric and magnetic fields, Schrödinger operators with random and almost periodic potentials and, finally, Schrödinger operator methods in differential geometry to prove the Morse inequalities and the index theorem
Orthogonal polynomials on the unit circle by
Barry Simon(
Book
)
24 editions published between 2004 and 2013 in English and Undetermined and held by 374 WorldCat member libraries worldwide
This twopart book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of onedimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by z (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line
24 editions published between 2004 and 2013 in English and Undetermined and held by 374 WorldCat member libraries worldwide
This twopart book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of onedimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by z (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line
Trace ideals and their applications by
Barry Simon(
Book
)
12 editions published in 1979 in English and held by 374 WorldCat member libraries worldwide
These expository lectures contain an advanced technical account of a branch of mathematical analysis. In his own lucid and readable style the author begins with a comprehensive review of the methods of bounded operators in a Hilbert space. He then goes on to discuss a wide variety of applications including Fredholm theory and more specifically his own specialty of mathematical quantum theory. included also are an extensive and uptodate list of references enabling the reader to delve more deeply into this topical subject
12 editions published in 1979 in English and held by 374 WorldCat member libraries worldwide
These expository lectures contain an advanced technical account of a branch of mathematical analysis. In his own lucid and readable style the author begins with a comprehensive review of the methods of bounded operators in a Hilbert space. He then goes on to discuss a wide variety of applications including Fredholm theory and more specifically his own specialty of mathematical quantum theory. included also are an extensive and uptodate list of references enabling the reader to delve more deeply into this topical subject
Functional integration and quantum physics by
Barry Simon(
Book
)
24 editions published between 1979 and 2014 in English and held by 281 WorldCat member libraries worldwide
The main theme of this classic book is the path integral technique and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of FeynmanKac formula. Starting with main examples of Gaussian processes, the author presents four different proofs of the FeynmanKac formula
24 editions published between 1979 and 2014 in English and held by 281 WorldCat member libraries worldwide
The main theme of this classic book is the path integral technique and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of FeynmanKac formula. Starting with main examples of Gaussian processes, the author presents four different proofs of the FeynmanKac formula
Spectral theory and mathematical physics : a festschrift in honor of Barry Simon's 60th birthday by
Fritz Gesztesy(
Book
)
24 editions published between 2007 and 2012 in English and held by 279 WorldCat member libraries worldwide
24 editions published between 2007 and 2012 in English and held by 279 WorldCat member libraries worldwide
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 252 WorldCat member libraries worldwide
13 editions published between 2013 and 2014 in English and held by 252 WorldCat member libraries worldwide
Quasiclassical methods by
Jeffrey Rauch(
Book
)
11 editions published in 1997 in English and held by 228 WorldCat member libraries worldwide
The chapters in this volume explore the various aspects of quasiclassical methods such as approximate theories for large Coulomb systems, Schroedinger operator with magnetic wells, ground state energy of heavy molecules in strong magnetic field, and methods with emphasis on coherent states. Included are also mathematical theories dealing with hpseudodifferential operators, asymptotic distribution of eigenvalues in gaps, a proof of the strong Scott conjecture, Lieb Thirring inequalities for the Pauli operator, and local trace formulae
11 editions published in 1997 in English and held by 228 WorldCat member libraries worldwide
The chapters in this volume explore the various aspects of quasiclassical methods such as approximate theories for large Coulomb systems, Schroedinger operator with magnetic wells, ground state energy of heavy molecules in strong magnetic field, and methods with emphasis on coherent states. Included are also mathematical theories dealing with hpseudodifferential operators, asymptotic distribution of eigenvalues in gaps, a proof of the strong Scott conjecture, Lieb Thirring inequalities for the Pauli operator, and local trace formulae
Loewner's theorem on monotone matrix functions by
Barry Simon(
)
10 editions published between 2019 and 2020 in English and held by 216 WorldCat member libraries worldwide
This book provides an in depth discussion of Loewner's theorem on the characterization of matrix monotone functions. The author refers to the book as a 'love poem,' one that highlights a unique mix of algebra and analysis and touches on numerous methods and results. The book details many different topics from analysis, operator theory and algebra, such as divided differences, convexity, positive definiteness, integral representations of function classes, Pick interpolation, rational approximation, orthogonal polynomials, continued fractions, and moreback cover
10 editions published between 2019 and 2020 in English and held by 216 WorldCat member libraries worldwide
This book provides an in depth discussion of Loewner's theorem on the characterization of matrix monotone functions. The author refers to the book as a 'love poem,' one that highlights a unique mix of algebra and analysis and touches on numerous methods and results. The book details many different topics from analysis, operator theory and algebra, such as divided differences, convexity, positive definiteness, integral representations of function classes, Pick interpolation, rational approximation, orthogonal polynomials, continued fractions, and moreback cover
Multiparticle quantum scattering with applications to nuclear, atomic, and molecular physics by
Donald G Truhlar(
Book
)
7 editions published in 1997 in English and held by 214 WorldCat member libraries worldwide
The topics in this volume include the ideas of mathematicians, physicists and chemists in the area of multiparticle scattering theory. Scattering theory (or collision theory as it is often called) is a fundamental area of theory and computation in both physics and chemistry. The correct formulation of scattering theory for twobody collisions is now well worked out, but systems with three or more particles still present fundamental unmet challenges, both in the formulations of the problem and in the interpretation of computational results. A key issue in the mathematical foundations is asymptotic completeness, which says that any state of a quantum system is a superposition of bound and scattering states. Key issues on the physical side are concerned with boundary conditions, electromagnetic fields, effective potentials and resonances
7 editions published in 1997 in English and held by 214 WorldCat member libraries worldwide
The topics in this volume include the ideas of mathematicians, physicists and chemists in the area of multiparticle scattering theory. Scattering theory (or collision theory as it is often called) is a fundamental area of theory and computation in both physics and chemistry. The correct formulation of scattering theory for twobody collisions is now well worked out, but systems with three or more particles still present fundamental unmet challenges, both in the formulations of the problem and in the interpretation of computational results. A key issue in the mathematical foundations is asymptotic completeness, which says that any state of a quantum system is a superposition of bound and scattering states. Key issues on the physical side are concerned with boundary conditions, electromagnetic fields, effective potentials and resonances
Methods of modern mathematical physics by
Michael Reed(
Book
)
63 editions published between 1972 and 2010 in English and Italian and held by 203 WorldCat member libraries worldwide
Methods of Modern Mathematical Physics, Volume I: Functional Analysis discusses the fundamental principles of functional analysis in modern mathematical physics. This book also analyzes the influence of mathematics on physics, such as the Newtonian mechanics used to interpret all physical phenomena. Organized into eight chapters, this volume starts with an overview of the functional analysis in the study of several concrete models. This book then discusses how to generalize the Lebesgue integral to work with functions on the real line and with Borel sets. This text also explores the proper
63 editions published between 1972 and 2010 in English and Italian and held by 203 WorldCat member libraries worldwide
Methods of Modern Mathematical Physics, Volume I: Functional Analysis discusses the fundamental principles of functional analysis in modern mathematical physics. This book also analyzes the influence of mathematics on physics, such as the Newtonian mechanics used to interpret all physical phenomena. Organized into eight chapters, this volume starts with an overview of the functional analysis in the study of several concrete models. This book then discusses how to generalize the Lebesgue integral to work with functions on the real line and with Borel sets. This text also explores the proper
Trace ideals and their applications by
Barry Simon(
Book
)
16 editions published between 2005 and 2014 in English and held by 194 WorldCat member libraries worldwide
"This is a second edition of a wellknown book on the theory of trace ideals in the algebra of operators in a Hilbert space. Because of the theory's many different applications, the book was widely used and much in demand. For this second edition, the author has added four chapters on the closely related theory of rank one perturbations of selfadjoint operators. He has also included a comprehensive index and an addendum describing some developments since the original notes were published."BOOK JACKET
16 editions published between 2005 and 2014 in English and held by 194 WorldCat member libraries worldwide
"This is a second edition of a wellknown book on the theory of trace ideals in the algebra of operators in a Hilbert space. Because of the theory's many different applications, the book was widely used and much in demand. For this second edition, the author has added four chapters on the closely related theory of rank one perturbations of selfadjoint operators. He has also included a comprehensive index and an addendum describing some developments since the original notes were published."BOOK JACKET
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Related Identities
 Reed, Michael 1942 Author Creator
 Wightman, A. S. (Arthur Strong) 19222013 Contributor Author Editor
 Lieb, Elliott H. Contributor Author Editor
 Bargmann, V. (Valentine) 19081989 Contributor Dedicatee
 Gesztesy, Fritz 1953 Other Honoree Dedicatee Editor
 Cycon, H. L. (Hans Ludwig) 1942 Other Author
 Beiglböck, E. 1939
 Leonhard, Woody Author
 Teschl, Gerald 1970 Editor
 Holden, H. (Helge) 1956 Author Editor
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Associated Subjects
Algebra Atoms Bargmann, V.(Valentine), ChemistryMathematics Chemometrics Compact groups Computer scienceMathematics Convex domains Differential equations Differential equationsNumerical solutions Diffusion Engineering mathematics Finite groups Forms, Quadratic Fourier analysis Functional analysis Functions of real variables Global analysis (Mathematics) Global differential geometry Group theory Hamiltonian operator Hilbert space Ideals (Algebra) Integration, Functional Lattice gas Lattice theory Manybody problem Mathematical analysis Mathematical physics Mathematical physicsAsymptotic theory Mathematics Matrices Monotonic functions Multiple scattering (Physics) Operator theory Orthogonal polynomials Particles (Nuclear physics) Physics Quantum computing Quantum field theory Quantum theory Representations of groups Scattering (Physics) Schrödinger operator Science Spectral theory (Mathematics) Statistical mechanics
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Alternative Names
Barry Simon Amerikaans wiskundige
Barry Simon amerikai matematikus, fizikus.
Barry Simon amerikansk fysiker och matematiker
Barry Simon amerikansk fysiker og matematiker
Barry Simon matamaiticeoir Meiriceánach
Barry Simon matemàtic estatunidenc
Barry Simon matematician american
Barry Simon matemático estadounidense
Barry Simon matematico statunitense
Barry Simon matematikan amerikan
Barry Simon mathématicien américain
Barry Simon USamerikanischer Mathematiker und Physiker
Barry Simon usona matematikisto
Saĭmon, B. 1946
Saĭmon, B. (Barri), 1946
Saĭmon, Barri 1946
Sajmon, B.
Sajmon, B. 1946
Sajmon, Barry 1946
Simon, B.
Simon, B. 1946
Simon, B. (Barry)
Simon, B. (Barry), 1946
Simon, Barry
Баррі Саймон
Саймон, Б.
Саймон, Б 1946
Саймон, Б. (Барри), 1946
Саймон, Барри
בארי סימון
בארי סימון מתמטיקאי אמריקאי
بارى سيمون
باري سيمون رياضياتي أمريكي
بری سیمون ریاضیدان و فیزیکدان آمریکایی
巴里·西蒙
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