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Microlocal Analysis and Precise Spectral Asymptotics

  • Book
  • © 1998

Overview

Authors:
  1. Victor Ivrii

    1. Department of Mathematics, University of Toronto, Toronto, Canada

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  • The pathbreaking work of Victor Ivrii in the last ten years represents very difficult mathematics.
  • Because of its technical difficulty and its size, it cannot be expected to sell to a large audience.
  • However for all those working on this subject,it will be a indispensable reference.

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XV
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  2. Introduction

    1. Introduction

      • Victor Ivrii
      Pages 1-17

  3. Semiclassical Microlocal Analysis

    1. Front Matter

      Pages 19-19
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    2. Introduction to Semiclassical Microlocal Analysis

      • Victor Ivrii
      Pages 21-52

    3. Propagation of Singularities in the Interior of a Domain

      • Victor Ivrii
      Pages 53-78

    4. Propagation of Singularities near the Boundary

      • Victor Ivrii
      Pages 79-117

  5. Estimates of the Spectrum

    1. Front Matter

      Pages 421-421
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    2. Estimates of the Negative Spectrum

      • Victor Ivrii
      Pages 423-450

    3. Estimates of the Spectrum in an Interval

      • Victor Ivrii
      Pages 451-478

  6. Asymptotics of Spectra

    1. Front Matter

      Pages 479-479
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    2. Weylian Asymptotics of Spectra

      • Victor Ivrii
      Pages 481-568

    3. Asymptotics of the Spectra of Schrödinger and Dirac Operators with Strong Magnetic Field

      • Victor Ivrii
      Pages 569-625

    4. Miscellaneous Asymptotics

      • Victor Ivrii
      Pages 627-707

  7. Back Matter

    Pages 709-733
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Keywords

About this book

The problem of spectral asymptotics, in particular the problem of the asymptotic dis­ tribution of eigenvalues, is one of the central problems in the spectral theory of partial differential operators; moreover, it is very important for the general theory of partial differential operators. I started working in this domain in 1979 after R. Seeley found a remainder estimate of the same order as the then hypothetical second term for the Laplacian in domains with boundary, and M. Shubin and B. M. Levitan suggested that I should try to prove Weyl's conjecture. During the past fifteen years I have not left the topic, although I had such intentions in 1985 when the methods I invented seemed to fai! to provide furt her progress and only a couple of not very exciting problems remained to be solved. However, at that time I made the step toward local semiclassical spectral asymptotics and rescaling, and new horizons opened.

Reviews

From the reviews:

"The monograph, under review, deals with one of the central problems in the spectral theory of partial differential operators, namely with the problem of spectral asymptotics, in particular with the problem of the asymptotic distribution of eigenvalues. … Summarizing, this is an excellent monograph on microlocal analysis, propagation of singularities and spectral asymptotics, based mainly on the author’s own results. It is warmly recommended to specialists in PDE’s, theoretical physics. The monograph will be useful also for advanced students." (Jeno Hegedus, Acta Scientiarum Mathematicarum, Vol. 74, 2008)

Authors and Affiliations

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Victor Ivrii

Bibliographic Information

  • Book Title: Microlocal Analysis and Precise Spectral Asymptotics

  • Authors: Victor Ivrii

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-12496-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Hardcover ISBN: 978-3-540-62780-7Published: 20 May 1998

  • Softcover ISBN: 978-3-642-08307-5Published: 04 December 2010

  • eBook ISBN: 978-3-662-12496-3Published: 14 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XV, 733

  • Topics: Partial Differential Equations

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