Microlocal Analysis and Precise Spectral Asymptotics / Edition 1

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Overview

Devoted to the methods of microlocal analysis applied to spectral asymptotics with accurate remainder estimates, this 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 Most of the results and their proofs are as yet unpublished.
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Editorial Reviews

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"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)

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Product Details

  • ISBN-13: 9783540627807
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 5/20/1998
  • Series: Springer Monographs in Mathematics Series
  • Edition description: 1998
  • Edition number: 1
  • Pages: 733
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.56 (d)

Table of Contents

Preface
0 Introduction 1
Pt. I Semiclassical Microlocal Analysis
1 Introduction to Semiclassical Microlocal Analysis 21
2 Propagation of Singularities in the Interior of a Domain 53
3 Propagation of Singularities near the Boundary 79
Pt. II Local and Microlocal Semiclassical Asymptotics
4 LSSA in the Interior of a Domain 121
5 Standard LSSA near the Boundary 219
6 Schrodinger Operators with Strong Magnetic Field 275
7 Dirac Operators with Strong Magnetic Field 367
Pt. III Estimates of the Spectrum
8 Estimates of the Negative Spectrum 423
9 Estimates of the Spectrum in an Interval 451
Pt. IV Asymptotics of Spectra
10 Weylian Asymptotics of Spectra 481
11 Schrodinger, Dirac Operators with Strong Magnetic Field 569
12 Miscellaneous Asymptotics 627
References 709
Index 725
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