Microlocal Analysis for Differential Operators
An Introduction

This book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.

Alain Grigis (Author), Johannes Sjöstrand (Author)

9780521449861, Cambridge University Press

Paperback, published 3 March 1994

160 pages
22.9 x 15.2 x 0.9 cm, 0.24 kg

"...an excellent introduction to microlocal analysis for graduate students and for mathematicians who wish to understand the basic ideas of calculus with classical pseudodifferential and Fourier integral operators....The exposition yields in an elegant form almost all basic tools related to microlocal analysis and it will be very helpful for any graduate student dealing with partial differential equations and mathematical physics." Vesselin M. Petkov, Mathematical Reviews

This short introduction to microlocal analysis is presented, in the spirit of Hörmander, 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 Sjöstrand 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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]