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Microlocal Analysis and Precise Spectral Asymptotics

  • Victor Ivrii

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Introduction

    1. Victor Ivrii
      Pages 1-17
  3. Semiclassical Microlocal Analysis

    1. Front Matter
      Pages 19-19
  4. Local and Microlocal Semiclassical Asymptotics

  5. Estimates of the Spectrum

    1. Front Matter
      Pages 421-421
    2. Victor Ivrii
      Pages 423-450
    3. Victor Ivrii
      Pages 451-478
  6. Asymptotics of Spectra

    1. Front Matter
      Pages 479-479
    2. Victor Ivrii
      Pages 481-568
    3. Victor Ivrii
      Pages 627-707
  7. Back Matter
    Pages 709-733

About this book

Introduction

Devoted to the methods of microlocal analysis applied to spectral asymptotics with accurate remainder estimates, this long awaited book develops the very powerful machinery of local and microlocal semiclassical spectral asymptotics, as well as methods of combining these asymptotics with spectral estimates. The rescaling technique, an easy to use and very powerful tool, is presented. Many theorems, considered till now as independent and difficult, are now just special cases of easy corollaries of the theorems proved in this book. Most of the results and their proofs are as yet unpublished. Part 1 considers semiclassical microlocal analysis and propagation of singularities inside the domain and near the boundary. Part 2 is on local and microlocal semiclassical spectral asymptotics for general operators and Schrödinger and Dirac operators. After a synthesis in Part 3, the real fun begins in Part 4: the main theorems are applied and numerous results, both known and new, are recovered with little effort. Then, in Chapter 12, non-Weyl asymptotics are obtained for operators in domains with thick cusps, degenerate operators, for spectral Riesz means for operators with singularities. Most of the results and almost all the proofs were never published.

Keywords

Dirac Microlocal analysis Semiclassical microlocal analysis Spectral asymptotics boundary element method field proof schrödinger operator theorem tool

Authors and affiliations

  • Victor Ivrii
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-12496-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08307-5
  • Online ISBN 978-3-662-12496-3
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site