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Microlocal Analysis for Differential Operators

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Microlocal Analysis for Differential Operators

Microlocal Analysis for Differential Operators

An Introduction
Alain Grigis, Université de Paris XIII
Johannes Sjöstrand, Université de Paris XI
May 1994
Paperback
9780521449861
AUD$101.95
inc GST
Paperback
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eBook
    Description

    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.

    Product details

    May 1994
    Paperback
    9780521449861
    160 pages
    229 × 152 × 9 mm
    0.24kg
    Available

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    Contents

    Table of Contents

    • 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.
      • Show more

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    About the authors
      Authors
    • Alain Grigis , Université de Paris XIII
    • Johannes Sjöstrand , Université de Paris XI

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