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...
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| Autor corporatiu: | |
| Format: | Electrònic eBook |
| Idioma: | English |
| Publicat: |
Boston, MA :
Birkhäuser Boston : Imprint: Birkhäuser,
2011.
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| Edició: | 1st ed. 2011. |
| Periòdiques: | Modern Birkhäuser Classics,
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| Matèries: | |
| Accés en línia: | https://doi.org/10.1007/978-0-8176-8108-1 |
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Taula de continguts:
- 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.