Helffer, Bernard
Overview
Works:  89 works in 261 publications in 2 languages and 4,430 library holdings 

Roles:  Author, Editor 
Classifications:  QA3, 515.72 
Publication Timeline
.
Most widely held works by
Bernard Helffer
Hypoelliptic estimates and spectral theory for FokkerPlanck operators and Witten Laplacians by
Bernard Helffer(
Book
)
20 editions published in 2005 in English and held by 304 WorldCat member libraries worldwide
There has recently been a renewal of interest in FokkerPlanck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not selfadjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global WeylHörmander pseudodifferential calculus, the spectral theory of nonselfadjoint operators, the semiclassical analysis of Schrödingertype operators, the Witten complexes and the Morse inequalities
20 editions published in 2005 in English and held by 304 WorldCat member libraries worldwide
There has recently been a renewal of interest in FokkerPlanck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not selfadjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global WeylHörmander pseudodifferential calculus, the spectral theory of nonselfadjoint operators, the semiclassical analysis of Schrödingertype operators, the Witten complexes and the Morse inequalities
Semiclassical analysis for the Schrödinger operator and applications by
Bernard Helffer(
Book
)
15 editions published in 1988 in English and held by 254 WorldCat member libraries worldwide
This introduction to semiclassical analysis is an extension of a course given by the author at the University of Nankai. It presents for some of the standard cases presented in quantum mechanics books a rigorous study of the tunneling effect, as an introduction to recent research work. The book may be read by a graduate student familiar with the classic book of ReedSimon, and for some chapters basic notions in differential geometry. The mathematician will find here a nice application of PDE techniques and the physicist will discover the precise link between approximate solutions (B.K.W. constructions) and exact eigenfunctions (in every dimension). An application to Witten's approach for the proof of the Morse inequalities is given, as are recent results for the Schrdinger operator with periodic potentials
15 editions published in 1988 in English and held by 254 WorldCat member libraries worldwide
This introduction to semiclassical analysis is an extension of a course given by the author at the University of Nankai. It presents for some of the standard cases presented in quantum mechanics books a rigorous study of the tunneling effect, as an introduction to recent research work. The book may be read by a graduate student familiar with the classic book of ReedSimon, and for some chapters basic notions in differential geometry. The mathematician will find here a nice application of PDE techniques and the physicist will discover the precise link between approximate solutions (B.K.W. constructions) and exact eigenfunctions (in every dimension). An application to Witten's approach for the proof of the Morse inequalities is given, as are recent results for the Schrdinger operator with periodic potentials
Hypoellipticité maximale pour des opérateurs polynomes de champs de vecteurs by
Bernard Helffer(
Book
)
11 editions published in 1985 in French and English and held by 201 WorldCat member libraries worldwide
11 editions published in 1985 in French and English and held by 201 WorldCat member libraries worldwide
Théorie spectrale pour des opérateurs globalement elliptiques by
Bernard Helffer(
Book
)
14 editions published between 1981 and 1984 in French and English and held by 158 WorldCat member libraries worldwide
14 editions published between 1981 and 1984 in French and English and held by 158 WorldCat member libraries worldwide
Semiclassical analysis, Witten Laplacians, and statistical mechanics by
Bernard Helffer(
Book
)
16 editions published in 2002 in English and held by 158 WorldCat member libraries worldwide
This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform LogSobolev inequality. Contents: Witten Laplacians Approach; Problems in Statistical Mechanics with Discrete Spins; Laplace Integrals and Transfer Operators; S
16 editions published in 2002 in English and held by 158 WorldCat member libraries worldwide
This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform LogSobolev inequality. Contents: Witten Laplacians Approach; Problems in Statistical Mechanics with Discrete Spins; Laplace Integrals and Transfer Operators; S
Spectral theory and its applications by
Bernard Helffer(
Book
)
13 editions published in 2013 in English and held by 156 WorldCat member libraries worldwide
"Bernard Helffer's graduatelevel introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non selfadjoint operator theory with an emphasis on the role of the pseudospectra"
13 editions published in 2013 in English and held by 156 WorldCat member libraries worldwide
"Bernard Helffer's graduatelevel introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non selfadjoint operator theory with an emphasis on the role of the pseudospectra"
Introduction to the semiclassical analysis for the Schrödinger operator and applications by
Bernard Helffer(
Book
)
2 editions published in 1988 in English and held by 137 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 137 WorldCat member libraries worldwide
Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach : the case with boundary by
Bernard Helffer(
Book
)
4 editions published in 2006 in English and held by 100 WorldCat member libraries worldwide
4 editions published in 2006 in English and held by 100 WorldCat member libraries worldwide
Résonances en limite semiclassique by
Bernard Helffer(
Book
)
9 editions published in 1986 in 3 languages and held by 97 WorldCat member libraries worldwide
9 editions published in 1986 in 3 languages and held by 97 WorldCat member libraries worldwide
Analyse semiclassique pour l'équation de Harper : (avec application à l'équation de Schrödinger avec champ magnétique) by
Bernard Helffer(
Book
)
15 editions published between 1988 and 1989 in French and English and held by 95 WorldCat member libraries worldwide
15 editions published between 1988 and 1989 in French and English and held by 95 WorldCat member libraries worldwide
Le papillon de Hofstadter revisité by
Bernard Helffer(
Book
)
8 editions published in 1990 in French and held by 86 WorldCat member libraries worldwide
8 editions published in 1990 in French and held by 86 WorldCat member libraries worldwide
Spectral methods in surface superconductivity by
Sren Fournais(
Book
)
14 editions published between 2009 and 2010 in English and Undetermined and held by 84 WorldCat member libraries worldwide
During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear GinzburgLandau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large GinzburgLandau parameter kappa. Key topics and features of the work: * Provides a concrete introduction to techniques in spectral theory and partial differential equations * Offers a complete analysis of the twodimensional GinzburgLandau functional with large kappa in the presence of a magnetic field * Treats the threedimensional case thoroughly * Includes open problems Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduatelevel understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semiclassical techniques in spectral theory that are involved in the nonlinear study of superconductivity
14 editions published between 2009 and 2010 in English and Undetermined and held by 84 WorldCat member libraries worldwide
During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear GinzburgLandau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large GinzburgLandau parameter kappa. Key topics and features of the work: * Provides a concrete introduction to techniques in spectral theory and partial differential equations * Offers a complete analysis of the twodimensional GinzburgLandau functional with large kappa in the presence of a magnetic field * Treats the threedimensional case thoroughly * Includes open problems Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduatelevel understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semiclassical techniques in spectral theory that are involved in the nonlinear study of superconductivity
Semiclassical analysis for Harper's equation III : Cantor structure of the spectrum by
Bernard Helffer(
Book
)
8 editions published between 1988 and 1990 in English and French and held by 84 WorldCat member libraries worldwide
8 editions published between 1988 and 1990 in English and French and held by 84 WorldCat member libraries worldwide
Analyse semiclassique pour l'équation de Harper : comportement semiclassique prés dún rationnel by
Bernard Helffer(
Book
)
9 editions published in 1990 in French and English and held by 82 WorldCat member libraries worldwide
9 editions published in 1990 in French and English and held by 82 WorldCat member libraries worldwide
Contributions à l'étude des opérateurs elliptiques et hypoelliptiques by
Bernard Helffer(
Book
)
7 editions published in 1977 in French and held by 77 WorldCat member libraries worldwide
7 editions published in 1977 in French and held by 77 WorldCat member libraries worldwide
Quantitative analysis of metastability in reversible diffusion processes via a witten complex apparoach : the case with boudary by
Bernard Helffer(
Book
)
1 edition published in 2006 in English and held by 18 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 18 WorldCat member libraries worldwide
Mathématiques à venir, dix ans après le Colloque de Palaiseau de 1987 : Chercheurs et enseignants en mathématiques : où
en eston à la veille de l'an 2000?(
Book
)
2 editions published in 1997 in French and held by 15 WorldCat member libraries worldwide
2 editions published in 1997 in French and held by 15 WorldCat member libraries worldwide
Semiclassical analysis for Schrödinger operators, Laplace integrals and transfer operators in large dimension : an introduction
: cours de DEA by
Bernard Helffer(
Book
)
3 editions published in 1995 in English and French and held by 14 WorldCat member libraries worldwide
3 editions published in 1995 in English and French and held by 14 WorldCat member libraries worldwide
PseudoDifferential Operators Quantization and Signals : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy,
June 1924, 2006 by Hans G Feichtinger(
)
1 edition published in 2008 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 11 WorldCat member libraries worldwide
Pseudodifferential operators : quantization and signals by
Hans G Feichtinger(
)
3 editions published in 2008 in English and held by 7 WorldCat member libraries worldwide
Pseudodifferential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudodifferential operators, Weyl transforms, Daubechies operators, Wick quantization and timefrequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted
3 editions published in 2008 in English and held by 7 WorldCat member libraries worldwide
Pseudodifferential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudodifferential operators, Weyl transforms, Daubechies operators, Wick quantization and timefrequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted
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Boundary value problems Differential equations, Partial Differential equations, PartialAsymptotic theory Differential operators Diffusion processes Eigenvalues Elliptic operators Fourier analysis Functional analysis Functions, Special Global analysis (Mathematics) Hypoelliptic operators Mathematical physics Mathematics MathematicsResearch MathematicsStudy and teaching Numerical analysis Operator theory Polynomial operators Pseudodifferential operators Quantum theory Resonance Schrödinger equation Schrödinger operator Spectral theory (Mathematics) Statistical mechanics Statistics Superconductivity Vector fields