| Titre de série : |
Introduction to pseudodifferential and Fourier integral operators, Volume 1 |
| Titre : |
Pseudodifferential Operators |
| Type de document : |
texte imprimé |
| Auteurs : |
François Trèves (1930-....), Auteur |
| Editeur : |
New York : Plenum Press |
| Année de publication : |
1980, cop. 1980 |
| Collection : |
The University series in mathematics, ISSN 1568-2676 |
| Importance : |
1 vol.(xxvii-299 p.) |
| Format : |
23 cm |
| ISBN/ISSN/EAN : |
978-1-4684-8782-4 |
| Note générale : |
PPN 183680480 - Reproduction de l'édition originale de : "New York : Plenum Press, 1980" - Sommaire (5 chap.) : Front Matter (Pages i-xxvii) - Standard Pseudodifferential Operators (Pages 1-81) - Special Topics and Applications (Pages 83-128) - Application to Boundary Problems for Elliptic Equations (Pages 129-216) - Pseudodifferential Operators of Type (?,?) (Pages 217-237) - Analytic Pseudodifferential Operators (Pages 239-299) - Back Matter (Pages xxix-xxxix) --- Egalement accessible en ligne sur le site de l'éditeur pour le personnel CNRS (ISTEX)
|
| Langues : |
Anglais (eng) |
| Tags : |
Fourier, Opérateurs intégraux de Opérateurs pseudo-différentiels Cauchy, Problème de Problèmes aux limites Equations différentielles elliptiques Fourier integral operators Pseudodifferential operators Cauchy problem Differential equations, Elliptic Boundary value problems |
| Index. décimale : |
515.723 Transformées (mathématiques)(Fourier, Hilbert, Laplace,Legendre, Z..) |
| Résumé : |
I have tried in this book to describe those aspects of pseudodifferential and Fourier integral operator theory whose usefulness seems proven and which, from the viewpoint of organization and "presentability," appear to have stabilized. Since, in my opinion, the main justification for studying these operators is pragmatic, much attention has been paid to explaining their handling and to giving examples of their use. Thus the theoretical chapters usually begin with a section in which the construction of special solutions of linear partial differential equations is carried out, constructions from which the subsequent theory has emerged and which continue to motivate it: parametrices of elliptic equations in Chapter I (introducing pseudodifferen tial operators of type 1, 0, which here are called standard), of hypoelliptic equations in Chapter IV (devoted to pseudodifferential operators of type p, 8), fundamental solutions of strongly hyperbolic Cauchy problems in Chap ter VI (which introduces, from a "naive" standpoint, Fourier integral operators), and of certain nonhyperbolic forward Cauchy problems in Chapter X (Fourier integral operators with complex phase). Several chapters-II, III, IX, XI, and XII-are devoted entirely to applications. Chapter II provides all the facts about pseudodifferential operators needed in the proof of the Atiyah-Singer index theorem, then goes on to present part of the results of A. Calderon on uniqueness in the Cauchy problem, and ends with a new proof (due to J. J. Kohn) of the celebrated sum-of-squares theorem of L. Hormander, a proof that beautifully demon strates the advantages of using pseudodifferential operators. |
| Note de contenu : |
Bibliogr. p. XXIX-XXXIV. Index |
| En ligne : |
https://link.springer.com/book/10.1007/978-1-4684-8780-0 |
Introduction to pseudodifferential and Fourier integral operators, Volume 1. Pseudodifferential Operators [texte imprimé] / François Trèves (1930-....), Auteur . - New York : Plenum Press, 1980, cop. 1980 . - 1 vol.(xxvii-299 p.) ; 23 cm. - ( The University series in mathematics, ISSN 1568-2676) . ISBN : 978-1-4684-8782-4 PPN 183680480 - Reproduction de l'édition originale de : "New York : Plenum Press, 1980" - Sommaire (5 chap.) : Front Matter (Pages i-xxvii) - Standard Pseudodifferential Operators (Pages 1-81) - Special Topics and Applications (Pages 83-128) - Application to Boundary Problems for Elliptic Equations (Pages 129-216) - Pseudodifferential Operators of Type (?,?) (Pages 217-237) - Analytic Pseudodifferential Operators (Pages 239-299) - Back Matter (Pages xxix-xxxix) --- Egalement accessible en ligne sur le site de l'éditeur pour le personnel CNRS (ISTEX)
Langues : Anglais ( eng)
| Tags : |
Fourier, Opérateurs intégraux de Opérateurs pseudo-différentiels Cauchy, Problème de Problèmes aux limites Equations différentielles elliptiques Fourier integral operators Pseudodifferential operators Cauchy problem Differential equations, Elliptic Boundary value problems |
| Index. décimale : |
515.723 Transformées (mathématiques)(Fourier, Hilbert, Laplace,Legendre, Z..) |
| Résumé : |
I have tried in this book to describe those aspects of pseudodifferential and Fourier integral operator theory whose usefulness seems proven and which, from the viewpoint of organization and "presentability," appear to have stabilized. Since, in my opinion, the main justification for studying these operators is pragmatic, much attention has been paid to explaining their handling and to giving examples of their use. Thus the theoretical chapters usually begin with a section in which the construction of special solutions of linear partial differential equations is carried out, constructions from which the subsequent theory has emerged and which continue to motivate it: parametrices of elliptic equations in Chapter I (introducing pseudodifferen tial operators of type 1, 0, which here are called standard), of hypoelliptic equations in Chapter IV (devoted to pseudodifferential operators of type p, 8), fundamental solutions of strongly hyperbolic Cauchy problems in Chap ter VI (which introduces, from a "naive" standpoint, Fourier integral operators), and of certain nonhyperbolic forward Cauchy problems in Chapter X (Fourier integral operators with complex phase). Several chapters-II, III, IX, XI, and XII-are devoted entirely to applications. Chapter II provides all the facts about pseudodifferential operators needed in the proof of the Atiyah-Singer index theorem, then goes on to present part of the results of A. Calderon on uniqueness in the Cauchy problem, and ends with a new proof (due to J. J. Kohn) of the celebrated sum-of-squares theorem of L. Hormander, a proof that beautifully demon strates the advantages of using pseudodifferential operators. |
| Note de contenu : |
Bibliogr. p. XXIX-XXXIV. Index |
| En ligne : |
https://link.springer.com/book/10.1007/978-1-4684-8780-0 |
|
Introduction to pseudodifferential and Fourier integral operators, Volume 1. Pseudodifferential Operators (1980, cop. 1980)
