Microlocal Analysis and Precise Spectral Asymptotics

Beschreibung:

Series: Springer Monographs in Mathematics. Num Pages: 748 pages, biography. BIC Classification: PBKF. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 38. Weight in Grams: 1134. . 2010. 1st ed. Softcover of orig. ed. 1998. Paperback. . . . . Books ship from the US and Ireland. Bestandsnummer des Verkäufers V9783642083075

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Inhaltsangabe:

Von der hinteren Coverseite: 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 Most of the results and their proofs are as yet unpublished.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.