Microlocal Analysis and Precise Spectral Asymptotics / Edition 1

Microlocal Analysis and Precise Spectral Asymptotics / Edition 1

by Victor Ivrii
     
 

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ISBN-10: 3642083072

ISBN-13: 9783642083075

Pub. Date: 12/03/2010

Publisher: Springer Berlin Heidelberg

This long awaited book is devoted to the methods of microlocal semiclassical analysis in application to spectral asymptotics with accurate remainder estimates. The very powerful machinery of local and microlocal semiclassical spectral asymptotics is developed as well as methods in combining these asymptotics with spectral estimates. The rescaling technique should

Overview

This long awaited book is devoted to the methods of microlocal semiclassical analysis in application to spectral asymptotics with accurate remainder estimates. The very powerful machinery of local and microlocal semiclassical spectral asymptotics is developed as well as methods in combining these asymptotics with spectral estimates. The rescaling technique should be mentioned as an easy as to use and very powerful tool. Many theorems, considered before as independent and difficult, now are just special cases of easy corollaries of the theorems proved in the book. Most of the results and almost all the proofs are as yet unpublished

Product Details

ISBN-13:
9783642083075
Publisher:
Springer Berlin Heidelberg
Publication date:
12/03/2010
Series:
Springer Monographs in Mathematics Series
Edition description:
Softcover reprint of hardcover 1st ed. 1998
Pages:
733
Product dimensions:
1.50(w) x 9.21(h) x 6.14(d)

Table of Contents

0. Introduction.- I. Semiclassical Microlocal Analysis.- 1. Introduction to Semiclassical Microlocal Analysis.- 2. Propagation of Singularities in the Interior of a Domain.- 3. Propagation of Singularities near the Boundary.- II. Local and Microlocal Semiclassical Asymptotics.- 4. LSSA in the Interior of a Domain.- 5. Standard LSSA near the Boundary.- 6. Schrödinger Operators with Strong Magnetic Field.- 7. Dirac Operators with Strong Magnetic Field.- III. Estimates of the Spectrum.- 8. Estimates of the Negative Spectrum.- 9. Estimates of the Spectrum in an Interval.- IV. Asymptotics of Spectra.- 10. Weylian Asymptotics of Spectra.- 11. Schrödinger, Dirac Operators with Strong Magnetic Field.- 12. Miscellaneous Asymptotics.- References.

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