Pseudodifferential operators and spectral theory / M. A. Shubin. Transl. from th - gebrauchtes Buch

EAN (ISBN-13): 9783540411956
ISBN (ISBN-10): 354041195X
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 1978
Herausgeber: Springer

Buch in der Datenbank seit 2007-05-15T10:04:40+02:00 (Berlin)
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ISBN/EAN: 354041195X

ISBN - alternative Schreibweisen:
3-540-41195-X, 978-3-540-41195-6
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: shubin, andersson, shub
Titel des Buches: pseudodifferential operator, pseudodifferential operators and spectral theory, moscow seen second, old russian, down and out moscow, for operators, springer mathematics, springer series, pseudo

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Daten vom Verlag:

Autor/in: M.A. Shubin
Titel: Pseudodifferential Operators and Spectral Theory
Verlag: Springer; Springer Berlin
288 Seiten
Erscheinungsjahr: 2001-07-03
Berlin; Heidelberg; DE
Sprache: Englisch
131,99 € (DE)

BC; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Eigenvalue; Fourier integral operator; Pseudodifferential operator; compactness; manifold; micolocal analysis spectral asymptotic; Analysis; Differential Geometry; Theoretical, Mathematical and Computational Physics; Differentielle und Riemannsche Geometrie; Mathematische Physik; BC; EA

I. Foundations of ?DO Theory.- § 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 TraceClass 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.