Fourier Integral OperatorsSpringer Science & Business Media, 3. stu 2010. - Broj stranica: 142 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. |
Sadržaj
Introduction | 1 |
Preliminaries | 8 |
Local Theory of Fourier Integrals | 23 |
Symplectic Differential Geometry | 45 |
Global Theory of Fourier Integral Operators | 91 |
Applications | 113 |
References | 138 |
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amplitude Aº(E asymptotic bicharacteristic curves bicharacteristic strips bijective called canonical relation canonical transformation Cauchy compact subset conic neighborhood coordinate coordinatization defined Definition denoted densities of order diag diffeomorphism distribution Duistermaat equal ess supp fiber follows Fourier integral operator global graph homogeneous canonical homogeneous of degree Hörmander implies intersection involutive isomorphism isotropic Lagrange space Lagrangian manifold Lagrangian subspace Lemma line bundle linear mapping linearly independent locally finite M₁ M₂ modulo n-dimensional nondegenerate nondegenerate phase function Note obtain operator of order oscillatory partition of unity principal symbol projection Proof properly supported Proposition pseudodifferential operator respectively satisfies Section sgn M1 sgn Q smooth solution Springer Science+Business Media strictly hyperbolic submanifold symplectic manifold symplectic vector space tangent space Tm(V transversal unique vector field wave front set WF(u