Fourier Integral Operators

• Κύριος συγγραφέας: Duistermaat, J.J (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston, 2011.
• Σειρά: Modern Birkhäuser Classics
• Θέματα: Mathematics.; Fourier analysis.; Integral equations.; Operator theory.; Partial differential equations.; Fourier Analysis.; Integral Equations.; Operator Theory.; Partial Differential Equations.

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...

Πίνακας περιεχομένων:

• 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.