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Microlocal Analysis for Differential Operators : An Introduction - Alain Grigis

Microlocal Analysis for Differential Operators

An Introduction

Paperback

Published: 2nd May 1994
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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.

"...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

Introductionp. 1
Symbols and oscillatory integralsp. 5
The method of stationary phasep. 19
Pseudodifferential operatorsp. 27
Application to elliptic operators and L[superscript 2] continuityp. 41
Local symplectic geometry I (Hamilton-Jacobi theory)p. 55
The strictly hyperbolic Cauchy problem--construction of a parametrixp. 67
The wavefront set (singular spectrum) of a distributionp. 77
Propagation of singularities for operators of real principle typep. 89
Local symplectic geometry IIp. 97
Canonical transformations of pseudodifferential operatorsp. 107
Global theory of Fourier integral operatorsp. 119
Spectral theory for elliptic operatorsp. 131
Bibliographyp. 145
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521449861
ISBN-10: 0521449863
Series: London Mathematical Society Lecture Notes
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 160
Published: 2nd May 1994
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.91 x 15.55  x 1.19
Weight (kg): 0.25