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" Microlocal Analysis and Precise Spectral Asymptotics "
by Victor Ivrii.
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BL
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| Record Number
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577814
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b407033
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| Main Entry
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Ivrii, Victor.
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| Title & Author
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Microlocal Analysis and Precise Spectral Asymptotics\ by Victor Ivrii.
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| Publication Statement
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Berlin, Heidelberg :: Springer Berlin Heidelberg :: Imprint: Springer,, 1998.
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| Series Statement
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Springer Monographs in Mathematics,
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| ISBN
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9783662124963
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: 9783642083075
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| Contents
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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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| Abstract
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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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| Subject
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Mathematics.
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| Subject
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Differential equations, Partial.
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SpringerLink (Online service)
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