Microlocal Analysis and Precise Spectral Asymptotics / Edition 1

Microlocal Analysis and Precise Spectral Asymptotics / Edition 1

by Victor Ivrii
     
 

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… See more details below

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 Most of the results and their proofs are as yet unpublished.

Product Details

ISBN-13:
9783540627807
Publisher:
Springer Berlin Heidelberg
Publication date:
05/20/1998
Series:
Springer Monographs in Mathematics Series
Edition description:
1998
Pages:
733
Product dimensions:
9.21(w) x 6.14(h) x 1.56(d)

Meet the Author

Table of Contents

Preface
0Introduction1
Pt. ISemiclassical Microlocal Analysis
1Introduction to Semiclassical Microlocal Analysis21
2Propagation of Singularities in the Interior of a Domain53
3Propagation of Singularities near the Boundary79
Pt. IILocal and Microlocal Semiclassical Asymptotics
4LSSA in the Interior of a Domain121
5Standard LSSA near the Boundary219
6Schrodinger Operators with Strong Magnetic Field275
7Dirac Operators with Strong Magnetic Field367
Pt. IIIEstimates of the Spectrum
8Estimates of the Negative Spectrum423
9Estimates of the Spectrum in an Interval451
Pt. IVAsymptotics of Spectra
10Weylian Asymptotics of Spectra481
11Schrodinger, Dirac Operators with Strong Magnetic Field569
12Miscellaneous Asymptotics627
References709
Index725

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