Maurice de Gosson – författare

JeanVaillant L'oeuvre de Jean Leray est originale et profonde; ses theoremes et ses theories sont au coeur des recherches mathematiques actuelles: la beaute de chacun de ses travaux ne se divise pas. Son cours de Princeton, sous forme de notes en anglais (et d'une traduction en russe) en est une belle illustration: ce cours presente les equations aux derivees partielles a partir de la transformation de Laplace et du theoreme de Cauchy-Kowaleska et contient l'essentiel de nombreusesrecherchesmodernes. Lerayavaitpourbutderesoudreunprobleme, souvent d'origine mecanique ou physique - qui se pose, et non qu'on se pose -, de demontrer un theoreme; il construit alors son oeuvre de facon complete et essentiellement intrinseque. En fait, Leray construit une theorie dont l'extension tient a son origine naturelle, l'acuite, la perfection, la profondeur d'esprit de son auteur;enmemetempsildominelescalculs,qu'ilmeneavecplaisiretelegance: "Il n'y a pas de mathematiques sans calculs" disait-il. La science etait au centre de la vie de Jean Leray. Il s'inquietait de sa sauvegarde. Rappelons quelques phrases de ses textes de 1974: "D'ailleurs la science ne s'apprend pas: elle se comprend.Elle n'est pas lettre morte et les livres n'assurent pas sa perennite; elle est une pensee vivante. Pour la maitriser notre esprit doit, habilement guide, la redecouvrir de meme que notre corps a du revivre dans le sein mat- nel, toute l'evolution qui crea notre espece. Aussi n'y a-t-il qu'une facon ef?cace d'enseigner les sciences et les techniques: transmettre l'esprit de recherche.

This book provides an in-depth and rigorous study of the Wigner transform and its variants. They are presented first within a context of a general mathematical framework, and then through applications to quantum mechanics. The Wigner transform was introduced by Eugene Wigner in 1932 as a probability quasi-distribution which allows expression of quantum mechanical expectation values in the same form as the averages of classical statistical mechanics. It is also used in signal processing as a transform in time-frequency analysis, closely related to the windowed Gabor transform.Written for advanced-level students and professors in mathematics and mathematical physics, it is designed as a complete textbook course providing analysis on the most important research on the subject to date. Due to the advanced nature of the content, it is also suitable for research mathematicians, engineers and chemists active in the field.

This book provides an in-depth and rigorous study of the Wigner transform and its variants. They are presented first within a context of a general mathematical framework, and then through applications to quantum mechanics. The Wigner transform was introduced by Eugene Wigner in 1932 as a probability quasi-distribution which allows expression of quantum mechanical expectation values in the same form as the averages of classical statistical mechanics. It is also used in signal processing as a transform in time-frequency analysis, closely related to the windowed Gabor transform.Written for advanced-level students and professors in mathematics and mathematical physics, it is designed as a complete textbook course providing analysis on the most important research on the subject to date. Due to the advanced nature of the content, it is also suitable for research mathematicians, engineers and chemists active in the field.

The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.

The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications.  New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations.  Some of the topics covered include:Abstract harmonic analysis,Numerical harmonic analysis,Sampling theory,Compressed sensing,Mathematical signal processing,Pseudodifferential operators, andApplications of harmonic analysis to quantum mechanics.Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.

The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications.  New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations.  Some of the topics covered include:Abstract harmonic analysis,Numerical harmonic analysis,Sampling theory,Compressed sensing,Mathematical signal processing,Pseudodifferential operators, andApplications of harmonic analysis to quantum mechanics.Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.

JeanVaillant L'oeuvre de Jean Leray est originale et profonde; ses theoremes et ses theories sont au coeur des recherches mathematiques actuelles: la beaute de chacun de ses travaux ne se divise pas. Son cours de Princeton, sous forme de notes en anglais (et d'une traduction en russe) en est une belle illustration: ce cours presente les equations aux derivees partielles a partir de la transformation de Laplace et du theoreme de Cauchy-Kowaleska et contient l'essentiel de nombreusesrecherchesmodernes. Lerayavaitpourbutderesoudreunprobleme, souvent d'origine mecanique ou physique - qui se pose, et non qu'on se pose -, de demontrer un theoreme; il construit alors son oeuvre de facon complete et essentiellement intrinseque. En fait, Leray construit une theorie dont l'extension tient a son origine naturelle, l'acuite, la perfection, la profondeur d'esprit de son auteur;enmemetempsildominelescalculs,qu'ilmeneavecplaisiretelegance: "Il n'y a pas de mathematiques sans calculs" disait-il. La science etait au centre de la vie de Jean Leray. Il s'inquietait de sa sauvegarde. Rappelons quelques phrases de ses textes de 1974: "D'ailleurs la science ne s'apprend pas: elle se comprend.Elle n'est pas lettre morte et les livres n'assurent pas sa perennite; elle est une pensee vivante. Pour la maitriser notre esprit doit, habilement guide, la redecouvrir de meme que notre corps a du revivre dans le sein mat- nel, toute l'evolution qui crea notre espece. Aussi n'y a-t-il qu'une facon ef?cace d'enseigner les sciences et les techniques: transmettre l'esprit de recherche.