Fourier integral operators
This volume is a useful introduction to the subject of Fourier integral operators and is based on the author's classic set of notes. Covering a range of topics from Hörmander s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes applications to hyp...
Gardado en:
| Autor Principal: | |
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| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2011. |
| Series: | Modern Birkhäuser Classics
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| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 23 avril 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Fourier integral operators, J.J. Duistermaat, Reprint of the 1996 edition, Boston, Birkhäuser, 2011, 1 vol. (X-142 p.), Modern Birkhäuser classics, 978-0-8176-8107-4 |
Table des matières:
- Preface 0. Introduction 1. Preliminaries 1.1 Distribution densities on manifolds 1.2 The method of stationary phase 1.3 The wave front set of a distribution 2. Local Theory of Fourier Integrals 2.1 Symbols 2.2 Distributions defined by oscillatory integrals 2.3 Oscillatory integrals with nondegenerate phase functions 2.4 Fourier integral operators (local theory) 2.5 Pseudodifferential operators in Rn 3. Symplectic Differential Geometry 3.1 Vector fields 3.2 Differential forms 3.3 The canonical 1- and 2-form T* (X) 3.4 Symplectic vector spaces 3.5 Symplectic differential geometry 3.6 Lagrangian manifolds 3.7 Conic Lagrangian manifolds 3.8 Classical mechanics and variational calculus 4. Global Theory of Fourier Integral Operators 4.1 Invariant definition of the principal symbol 4.2 Global theory of Fourier integral operators 4.3 Products with vanishing principal symbol 4.4 L2-continuity 5. Applications 5.1 The Cauchy problem for strictly hyperbolic differential operators with C-infinity coefficients 5.2 Oscillatory asymptotic solutions. Caustics References