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Viser: Pseudodifferential Operators and Spectral Theory
Pseudodifferential Operators and Spectral Theory
M. A. Shubin og Stig I. Andersson
(2001)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- 2. Udgave
- Paperback
- Udgiver: Springer Berlin / Heidelberg (Juli 2001)
- Forfattere: M. A. Shubin og Stig I. Andersson
- ISBN: 9783540411956
1. Oscillatory Integrals.- §
2. Fourier Integral Operators (Preliminaries).- §
3. The Algebra of Pseudodifferential Operators and Their Symbols.- §
4. Change of Variables and Pseudodifferential Operators on Manifolds.- §
5. Hypoellipticity and Ellipticity.- §
6. Theorems on Boundedness and Compactness of Pseudodifferential Operators.- §
7. The Sobolev Spaces.- §
8. The Fredholm Property, Index and Spectrum.- II. Complex Powers of Elliptic Operators.- §
9. Pseudodifferential Operators with Parameter. The Resolvent.- §
10. Definition and Basic Properties of the Complex Powers of an Elliptic Operator.- §
11. The Structure of the Complex Powers of an Elliptic Operator.- §
12. Analytic Continuation of the Kernels of Complex Powers.- §
13. The ?-Function of an Elliptic Operator and Formal Asymptotic Behaviour of the Spectrum.- §
14. The Tauberian Theorem of Ikehara.- §
15. Asymptotic Behaviour of the Spectral Function and the Eigenvalues (Rough Theorem).- III. Asymptotic Behaviour of the Spectral Function.- §
16. Formulation of the Hormander Theorem and Comments.- §
17. Non-linear First Order Equations.- §
18. The Action of a Pseudodifferential Operator on an Exponent.- §
19. Phase Functions Defining the Class of Pseudodifferential Operators.- §
20. The Operator exp(-- it A).- § 2l. Precise Formulation and Proof of the Hormander Theorem.- §
22. The Laplace Operator on the Sphere.- IV. Pseudodifferential Operators in ?n.- §
23. An Algebra of Pseudodifferential Operators in ?n.- §
24. The Anti-Wick Symbol. Theorems on Boundedness and Compactness.- §
25. Hypoellipticity and Parametrix. Sobolev Spaces. The Fredholm Property.- §
26. Essential Self-Adjointness. Discreteness of the Spectrum.- §
27. Trace and Trace Class Norm.- §
28. The Approximate Spectral Projection.- §
29. Operators with Parameter.- §
30. Asymptotic Behaviour ofthe Eigenvalues.- Appendix
1. Wave Fronts and Propagation of Singularities.- Appendix
2. Quasiclassical Asymptotics of Eigenvalues.- Appendix
3. Hilbert-Schmidt and Trace Class Operators.- A Short Guide to the Literature.- Index of Notation.