Fourier Integral OperatorsSpringer Science & Business Media, 3 nov. 2010 - 142 pages More than twenty years ago I gave a course on Fourier Integral Op erators at the Catholic University of Nijmegen (1970-71) from which a set of lecture notes were written up; the Courant Institute of Mathematical Sciences in New York distributed these notes for many years, but they be came increasingly difficult to obtain. The current text is essentially a nicely TeXed version of those notes with some minor additions (e.g., figures) and corrections. Apparently an attractive aspect of our approach to Fourier Integral Operators was its introduction to symplectic differential geometry, the basic facts of which are needed for making the step from the local definitions to the global calculus. A first example of the latter is the definition of the wave front set of a distribution in terms of testing with oscillatory functions. This is obviously coordinate-invariant and automatically realizes the wave front set as a subset of the cotangent bundle, the symplectic manifold in which the global calculus takes place. |
Table des matières
Introduction
| 1 |
Preliminaries
| 8 |
Local Theory of Fourier Integrals
| 23 |
Symplectic Differential Geometry
| 45 |
Global Theory of Fourier Integral Operators
| 91 |
Applications
| 113 |
| 138 | |
Autres éditions - Tout afficher
Expressions et termes fréquents
amplitude applied assume asymptotic bundle called canonical choose closed compact complex condition cone conic connected constant construction contained continuous Conversely coordinate defined Definition denoted depend diffeomorphism differential differential operator distribution equal equivalent example exists fact fiber finally follows Fourier integral operator given global graph Hamilton hence homogeneous function homogeneous of degree hyperbolic implies independent induced intersection invariant Lagrange manifold Lagrangian leads Lemma linear mapping locally manifold means Moreover multiplication neighborhood Note obtain points positive principal symbol problem projection Proof properly Proposition prove pseudodifferential operator regarded relation remark respectively satisfies shows smooth solution strips submanifold subset subspace supp supported Suppose symplectic taking tangent space Theorem theory transformation transversal unique vector field vector space wave write