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 application to hyperbolic equations(= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially inwave propagation, rep. WKB-methods. Familiarity with analysis (distributions and Fourier transformation) and differential geometry is useful. Additionally,this book is designed for a one-semester introductory course on Fourier integral operators aimed at a broad audience. Based on author’s original lecture notes Covers a broad range of topics Useful for both practitioners and students Applications put theory in context INDICE: Preface.- 0. Introduction.- 1. Preliminaries.- 1.1 Distribution densities on manifolds.- 1.2 The method of stationary phase.- 1.3 The wave frontset of a distribution.- 2. Local Theory of Fourier Integrals.- 2.1 Symbols.- 2.2 Distributions defined by oscillatory integrals.- 2.3 Oscillatory integralswith 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- and2-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 IntegralOperators.- 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 strictlyhyperbolic differential operators with C-infinity coefficients.- 5.2 Oscillatory asymptotic solutions. Caustics.- References.
- ISBN: 978-0-8176-8107-4
- Editorial: Birkhaüser
- Encuadernacion: Rústica
- Páginas: 142
- Fecha Publicación: 29/11/2010
- Nº Volúmenes: 1
- Idioma: Inglés