Microlocal Analysis and Precise Spectral Asymptotics
(Sprache: Englisch)
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...
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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.
Inhaltsverzeichnis zu „Microlocal Analysis and Precise Spectral Asymptotics “
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.
Bibliographische Angaben
- Autor: Victor Ivrii
- 1998, 733 Seiten, 1 Schwarz-Weiß-Abbildungen, Maße: 15,9 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3540627804
- ISBN-13: 9783540627807
- Erscheinungsdatum: 20.05.1998
Sprache:
Englisch
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