Alain Grigis

Microlocal Analysis for Differential Operators (eBook, PDF)

An Introduction

• Format: PDF

Produktbeschreibung

This short introduction to microlocal analysis is presented, in the spirit of Hormander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjostrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 3. März 1994
• Englisch
• ISBN-13: 9781107108479
• Artikelnr.: 52839580

Inhaltsangabe

Introduction
1. Symbols and oscillatory integrals
2. The method of stationary phase
3. Pseudodifferential operators
4. Application to elliptic operators and L2 continuity
5. Local symplectic geometry I (Hamilton-Jacobi theory)
6. The strictly hyperbolic Cauchy problem - construction of a parametrix
7. The wavefront set (singular spectrum) of a distribution
8. Propagation of singularities for operators of real principle type
9. Local symplectic geometry II
10. Canonical transformations of pseudodifferential operators
11. Global theory of Fourier integral operators
12. Spectral theory for elliptic operators
Bibliography.