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£73.03

Springer Microlocal Analysis and Precise Spectral Asymptotics (Springer Monographs in Mathematics)

Name: Microlocal Analysis and Precise Spectral Asymptotics (Springer Monographs in Mathematics)
Brand: Springer
Price: 73.03 GBP
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Differential Equations

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Description

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 Most of the results and almost all the proofs are as yet unpublished Review From the reviews: "The monograph, under review, deals with one of the central problems in the spectral theory of partial differential operators, namely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) From the Back Cover 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 Most of the results and their proofs are as yet unpublished.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.

Product Specifications

Brand: Springer
Format: paperback
ASIN: 3642083072
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Differential Equations
Domain: Amazon UK
Release Date: 04 December 2010
Listed Since: 20 September 2010

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Springer Microlocal Analysis and Precise Spectral Asymptotics (Springer Monographs in Mathematics)

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