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Louis Boutet de Monvel, selected works

Author: L Boutet de Monvel; Victor Guillemin; J Sjöstrand
Publisher: Cham : Springer, 2017.
Series: Contemporary mathematicians.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book features a selection of articles by Louis Boutet de Monvel and presents his contributions to the theory of partial differential equations and analysis. The works selected here reveal his central role in the development of his field, including three cornerstones: firstly, analytic pseudodifferential operators, which have become a fundamental aspect of analytic microlocal analysis, and secondly the Boutet de  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Guillemin, Victor W.
Louis Boutet de Monvel, Selected Works.
Cham : Springer International Publishing, ©2017
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: L Boutet de Monvel; Victor Guillemin; J Sjöstrand
ISBN: 9783319279091 3319279092
OCLC Number: 987075864
Description: 1 online resource (855 pages).
Contents: 1: Introduction; 1.1 Boundary Value Problems; 1.2 Analytic Pseudodifferential Operators; 1.3 Operators with Multiple Characteristics; 1.4 Index Theory; 1.5 The CR-Embedding Theorem; 1.6 Zoll Manifolds; 1.7 Bergman Kernels; 1.8 Star Products; 1.9 Conclusion; References; 2: Louis Boutet deMonvel 1941-2014; 2.1 Biography; 2.2 Impressions of Louis Boutet de Monvel's Life; 3: Les travaux de Louis Boutet de Monvel sur les opérateurs pseudodifférentiels et le théorème de l'indice; References; 4: Elliptic Boundary Problems; 4.1 Commentary by Gerd Grubb. TheWorks of L. Boutet de Monvel on Elliptic Boundary Value Problems; References; 4.2 Comportement d'un opérateur pseudo-différentiel sur une variété à bord. I. La propriété de transmission; Comportement d'un opérateur pseudo-différentiel sur une variété à bord. I. La propriété de transmission; 1. La propriete de transmission; 2. Application a certains operateurs pseudo-diffe rentiels de convolution; BIBLIOGRAPHIE; 4.3 Comportement d'un opérateur pseudo-différentiel sur une variété à bord. II. Pseudo-noyaux de Poisson. Comportement d'un opérateur pseudo-différentiel sur une variété à bord. II. Pseudo-noyaux de Poisson; Notations: 0. Rappels sur les operateurs pseudo-differentiels; Propriete des operatcurs pseudo-differentiels; 1. Pseudo noyaux de Poisson sur une variete a bord; Proprietes des pseudo noyaux de Poisson; 2. Comportement d'un operateur pseudo-diffcrentiel au voisinage d'une hyper-surface; 3 Appendice; Calcul du symbole de K et G; Application aux problemes aux limites; REFERENCES; 4.4 Opérateurs pseudo-différentiels analytiques et problèmes aux limites elliptiques. Opérateurs pseudo-différentiels analytiques et problèmes aux limites elliptiques; CHAPITRE I: LES OPERATEURS ET LE CALCUL SYMBOLIQUE; 0. Notations; 1. Notations particulieres a Rn; 1. Les operateurs negligeables analytiques; 2. Les operateurs pseudo-differentiels analytiques de type u (d'apres L. Hormander); 2. Nous en arrivons au but de ce paragraphe; 3. Operateurs de Poisson analytiques; I. Un exemple fondamental; 2. Noyaux de Poisson analytiques elementaires; 3. Noyaux de Poisson analytiques; 4. Symbole et representation par integrale de Fourier; 5. Proprietes de continuite. 6. Noyaux de Poisson generalises; 4. Operateurs Trace analytiques; 5. Noyaux de Green singuliers analytiques; 6. Composition et calcul symbolique; 7. L'algebre des operateurs pseudo-differentiels. Operateurs generalises et transposition; 1. Operateurs pseudo-diflerentiels sur Q; 2. Classe d'un operateur pseudo-differentiel; 3. Transposes. Formule de Green; 4. Terminons par les remarques suivantes; 7. Operateurs a symbole G; CHAPITRE II: Applications; 1. Solutions d'un operateur differentiel elliptique a coefficients analytiques sur une variete a bord compacte; 2. Un exemple. 3. Etude du cas general.
Series Title: Contemporary mathematicians.
Responsibility: Victor W. Guillemin, Johannes Sjöstrand, editors.

Abstract:

This book features a selection of articles by Louis Boutet de Monvel and presents his contributions to the theory of partial differential equations and analysis. The works selected here reveal his central role in the development of his field, including three cornerstones: firstly, analytic pseudodifferential operators, which have become a fundamental aspect of analytic microlocal analysis, and secondly the Boutet de Monvel calculus for boundary problems for elliptic partial differential operators, which is still an important tool also in index theory. Thirdly, Boutet de Monvel was one of the first people to recognize the importance of the existence of generalized functions, whose singularities are concentrated on a single ray in phase space, which led him to make essential contributions to hypoelliptic operators and to a very successful and influential calculus of Toeplitz operators with applications to spectral and index theory. Other topics treated here include microlocal analysis, star products and deformation quantization as well as problems in several complex variables, index theory and geometric quantization. This book will appeal to both experts in the field and students who are new to this subject.

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