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

Ivrii, Victor

 
9783642083075: Microlocal Analysis and Precise Spectral Asymptotics (Springer Monographs in Mathematics)
Tapa blanda
ISBN 10: 3642083072 ISBN 13: 9783642083075
Editorial: Springer, 2010

Sinopsis

The problem of spectral asymptotics, in particular the problem of the asymptotic dis­ tribution of eigenvalues, is one of the central problems in the spectral theory of partial differential operators; moreover, it is very important for the general theory of partial differential operators. I started working in this domain in 1979 after R. Seeley found a remainder estimate of the same order as the then hypothetical second term for the Laplacian in domains with boundary, and M. Shubin and B. M. Levitan suggested that I should try to prove Weyl’s conjecture. During the past fifteen years I have not left the topic, although I had such intentions in 1985 when the methods I invented seemed to fai! to provide furt her progress and only a couple of not very exciting problems remained to be solved. However, at that time I made the step toward local semiclassical spectral asymptotics and rescaling, and new horizons opened.

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De la contraportada

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 Most of the results and their proofs are as yet unpublished.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

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Editorial
Springer
Año de publicación
2010
Idioma
Inglés
ISBN 10 
3642083072
ISBN 13 
9783642083075
Encuadernación
Tapa blanda
Número de páginas
752
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9783540627807: Microlocal Analysis and Precise Spectral Asymptotics (Springer Monographs in Mathematics)

Edición Destacada

ISBN 10:  3540627804 ISBN 13:  9783540627807
Editorial: Springer, 1998
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