WorldCat Identities

Helffer, Bernard

Overview
Works: 85 works in 290 publications in 3 languages and 4,810 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Editor, Thesis advisor, 956, Opponent
Classifications: QA3, 515.72
Publication Timeline
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Most widely held works by Bernard Helffer
Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians by Bernard Helffer( Book )

23 editions published in 2005 in English and held by 313 WorldCat member libraries worldwide

There has recently been a renewal of interest in Fokker-Planck 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 self-adjoint 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 Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes and the Morse inequalities
Semi-classical analysis for the Schrödinger operator and applications by Bernard Helffer( Book )

18 editions published in 1988 in English and Undetermined and held by 270 WorldCat member libraries worldwide

This introduction to semi-classical 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 Reed-Simon, 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 )

14 editions published in 1985 in 3 languages and held by 212 WorldCat member libraries worldwide

Spectral theory and its applications by Bernard Helffer( Book )

17 editions published in 2013 in English and Undetermined and held by 180 WorldCat member libraries worldwide

"Bernard Helffer's graduate-level 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 self-adjoint operator theory with an emphasis on the role of the pseudospectra"--
Semiclassical analysis, Witten Laplacians, and statistical mechanics by Bernard Helffer( Book )

17 editions published in 2002 in English and held by 174 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 Log-Sobolev inequality
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 167 WorldCat member libraries worldwide

Introduction to the semi-classical analysis for the Schrödinger operator and applications by Bernard Helffer( Book )

2 editions published in 1988 in English and held by 127 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 )

7 editions published in 2006 in English and German and held by 106 WorldCat member libraries worldwide

Analyse semi-classique pour l'équation de Harper : (avec application à l'équation de Schrödinger avec champ magnétique) by Bernard Helffer( Book )

18 editions published between 1988 and 1989 in French and English and held by 103 WorldCat member libraries worldwide

Résonances en limite semi-classique by Bernard Helffer( Book )

11 editions published in 1986 in 3 languages and held by 100 WorldCat member libraries worldwide

Le papillon de Hofstadter revisité by Bernard Helffer( Book )

11 editions published in 1990 in French and English and held by 95 WorldCat member libraries worldwide

Spectral methods in surface superconductivity by Søren Fournais( Book )

18 editions published between 2009 and 2010 in English and Undetermined and held by 91 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 Ginzburg{u2013}Landau 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 Ginzburg{u2013}Landau 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 two-dimensional Ginzburg{u2013}Landau functional with large kappa in the presence of a magnetic field * Treats the three-dimensional case thoroughly * Includes open problems Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level 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 semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity
Semi-classical analysis for Harper's equation III : Cantor structure of the spectrum by Bernard Helffer( Book )

14 editions published between 1988 and 1990 in 3 languages and held by 90 WorldCat member libraries worldwide

Contributions à l'étude des opérateurs elliptiques et hypoelliptiques by Bernard Helffer( Book )

8 editions published in 1977 in French and held by 80 WorldCat member libraries worldwide

Pseudo-differential operators : quantization and signals : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-24, 2006 by Hans G Feichtinger( )

5 editions published in 2008 in English and held by 20 WorldCat member libraries worldwide

Pseudo-differential 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 pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted
Analyse semi-classique pour l'équation de Harper : comportement semi-classique prés dún rationnel by Bernard Helffer( Book )

4 editions published in 1990 in French and English and held by 17 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

Hypoellipticité pour des classes d'opérateurs pseudodifférentiels à caractéristiques multiples by Bernard Helffer( Book )

4 editions published in 1976 in French and Undetermined and held by 10 WorldCat member libraries worldwide

Semiclassical Analysis, Witten Laplacians, and Statistical Mechanics by Bernard Helffer( )

2 editions published in 2002 in English and held by 0 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 Log-Sobolev inequality. Contents: Witten Laplacians Approach; Problems in Statistical Mechanics with Discrete Spins; Laplace Integrals and Transfer Operators; S
 
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Audience level: 0.64 (from 0.03 for Semiclassi ... to 0.93 for Hypoellipt ...)

Semi-classical analysis for the Schrödinger operator and applicationsIntroduction to the semi-classical analysis for the Schrödinger operator and applications
Alternative Names
Bernard Helffer Frans wiskundige

Bernard Helffer französischer Mathematiker

Bernard Helffer French mathematician

Helffer, B.

Helffer, B. 1949-

Helffer, B. (Bernard)

Helffer, Bernard

Languages
English (125)

French (79)

German (1)

Covers
Semi-classical analysis for the Schrödinger operator and applicationsSemiclassical analysis, Witten Laplacians, and statistical mechanicsIntroduction to the semi-classical analysis for the Schrödinger operator and applicationsQuantitative analysis of metastability in reversible diffusion processes via a Witten complex approach : the case with boundarySpectral methods in surface superconductivityPseudo-differential operators : quantization and signals : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-24, 2006