Springer Monographs in Mathematics

Microlocal Analysis and Precise Spectral Asymptotics

Authors: Ivrii, Victor

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  • ISBN 978-3-662-12496-3
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About this book

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 Most of the results and their proofs are as yet unpublished.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.

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)


Table of contents (13 chapters)

  • Introduction

    Ivrii, Victor

    Pages 1-17

  • Introduction to Semiclassical Microlocal Analysis

    Ivrii, Victor

    Pages 21-52

  • Propagation of Singularities in the Interior of a Domain

    Ivrii, Victor

    Pages 53-78

  • Propagation of Singularities near the Boundary

    Ivrii, Victor

    Pages 79-117

  • Standard Local Semiclassical Spectral Asymptotics in the Interior of a Domain

    Ivrii, Victor

    Pages 121-217

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-662-12496-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-540-62780-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • ISBN 978-3-642-08307-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Microlocal Analysis and Precise Spectral Asymptotics
Authors
Series Title
Springer Monographs in Mathematics
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-12496-3
DOI
10.1007/978-3-662-12496-3
Hardcover ISBN
978-3-540-62780-7
Softcover ISBN
978-3-642-08307-5
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XV, 733
Topics