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Viser: Fourier Integral Operators
Fourier Integral Operators
J. J. Duistermaat
(2010)
Sprog: Engelsk
Detaljer om varen
- Paperback: 154 sider
- Udgiver: Birkhäuser Boston (November 2010)
- ISBN: 9780817681074
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.