Microlocal Analysis and Precise Spectral Asymptotics
Author:   Victor Ivrii
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition:   Softcover reprint of hardcover 1st ed. 1998
ISBN:  

9783642083075


Pages:   733
Publication Date:   04 December 2010
Format:   Paperback
Availability:   In Print   Availability explained
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Microlocal Analysis and Precise Spectral Asymptotics


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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 Most of the results and almost all the proofs are as yet unpublished

Full Product Details

Author:   Victor Ivrii
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 1998
Dimensions:   Width: 15.50cm , Height: 3.80cm , Length: 23.50cm
Weight:   1.134kg
ISBN:  

9783642083075


ISBN 10:   3642083072
Pages:   733
Publication Date:   04 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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.

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)


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