Microlocal Analysis for Differential Operators: An Introduction

ISBN-13: 9780521449861 / Angielski / Miękka / 1994 / 160 str.

Alain Grigis; Johannes Sjostrand

Opis

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 emphasize the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions.

Recenzje

"...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

Spis treści

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.