Microlocal analysis for differential operators : an introduction / Alain Grigis, Johannes Sjöstrand.

Format:

Book

Author/Creator:

Grigis, Alain, author.

Sjöstrand, J. (Johannes), author.

Series:

London Mathematical Society lecture note series ; 196.

London Mathematical Society lecture note series ; 196

Language:

English

Subjects (All):

Differential operators.

Microlocal analysis.

Physical Description:

1 online resource (151 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1994.

Summary:

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.

Contents:

1. Symbols and oscillatory integrals

2. The method of stationary phase

3. Pseudodifferential operators

4. Application to elliptic operators and L[superscript 2] 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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 145-148) and indexes.

ISBN:

1-139-88492-1

1-107-10051-8

1-107-10299-5

1-107-08856-9

1-107-09474-7

1-107-09149-7

0-511-72144-7