Dieudonné / Eilenberg / Bass Treatise on Analysis

Volume 10 in International Series of Monographs on Pure and Applied Mathematics
1. Auflage 2014
ISBN: 978-1-4831-4496-2
Verlag: Elsevier Reference Monographs
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 387 Seiten

Treatise on Analysis, Volume 10-VII provides information pertinent to the fundamental aspects of linear functional equations. This book discusses the problems dealing with functional equations of scalar or of vectors.
Comprised of one chapter, this volume begins with a description and study of the primary concepts and tools that have prompted the progress in the study of linear partial differential equations. This text then explains the importance of the integral operators. The reader is also introduced to integral operators that operate not only on vector function, but also on sections of vector bundles. This book discusses as well the applications of the differential operators to spectral theory.
This book is a valuable resource for mathematicians.

Autoren/Hrsg.

Dieudonné, J.

Eilenberg, Samuel

Bass, Hyman

Inhaltsverzeichnis

1;Front Cover;1
2;Treatise on Analysis;4
3;Copyright Page;5
4;Table of Contents;6
5;NOTATION;8
6;CHAPTER XXIII.
LINEAR FUNCTIONAL EQUATIONS;16
6.1;PART I: PSEUDODIFFERENTIAL OPERATORS;16
6.1.1;1. INTEGRAL OPERATORS;22
6.1.2;2. INTEGRAL OPERATORS OF PROPER TYPE;25
6.1.3;3. INTEGRAL OPERATORS ON VECTOR BUNDLES;31
6.1.4;4. DENSITY BUNDLE AND KERNEL SECTIONS;35
6.1.5;5. BOUNDED SECTIONS;44
6.1.6;6. VOLTERRA OPERATORS;47
6.1.7;7. CARLEMAN OPERATORS;54
6.1.8;8. GENERALIZED EIGENFUNCTIONS;68
6.1.9;9. KERNEL DISTRIBUTIONS;77
6.1.10;10. REGULAR KERNEL DISTRIBUTIONS;90
6.1.11;11. SMOOTHING OPERATORS AND COMPOSITION OF OPERATORS;96
6.1.12;12. WAVE FRONT OF A DISTRIBUTION;110
6.1.13;13. CONVOLUTION EQUATIONS;120
6.1.14;14. ELEMENTARY SOLUTIONS;129
6.1.15;15. PROBLEMS OF EXISTENCE AND UNIQUENESS FOR SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS;140
6.1.16;16. OPERATOR SYMBOLS;156
6.1.17;17. OSCILLATING INTEGRALS;167
6.1.18;18. LAX–MASLOV OPERATORS;179
6.1.19;19. PSEUDO-DIFFERENTIAL OPERATORS;185
6.1.20;20. SYMBOL OF A PSEUDODIFFERENTIAL OPERATOR OF PROPER TYPE;198
6.1.21;21. MATRIX PSEUDODIFFERENTIAL OPERATORS;209
6.1.22;22. PARAMETRIX OF ELLIPTICAL OPERATORS ON AN OPEN SUBSET OF Rn;212
6.1.23;23. PSEUDODIFFERENTIAL OPERATORS IN Hso(X) SPACES;228
6.1.24;24. CLASSICAL DIRICHLET PROBLEM AND COARSE DIRICHLET PROBLEMS;247
6.1.25;25. THE GREEN OPERATOR;257
6.1.26;26. PSEUDODIFFERENTIAL OPERATORS ON A MANIFOLD;263
6.1.27;27. ADJOINT OF A PSEUDODIFFERENTIAL OPERATOR ON A MANIFOLD. COMPOSITION OF TWO PSEUDODIFFERENTIAL OPERATORS ON A MANIFOLD;270
6.1.28;28. EXTENSION OF PSEUDODIFFERENTIAL OPERATORS TO DISTRIBUTION SECTIONS;277
6.1.29;29. PRINCIPAL SYMBOLS;285
6.1.30;30. PARAMETRIX OF ELLIPTIC OPERATORS ON MANIFOLDS;291
6.1.31;31. SPECTRAL THEORY OF HERMITIAN ELLIPTIC OPERATORS: I. SELF-ADJOINT EXTENSIONS AND BOUNDARY CONDITIONS;305
6.1.32;32. SPECTRAL THEORY OF HERMITIAN ELLIPTIC OPERATORS: II. GENERALIZED EIGENFUNCTIONS;312
6.1.33;33. ESSENTIALLY SELF-ADJOINT PSEUDODIFFERENTIAL OPERATORS: I. HERMITIAN CONVOLUTION OPERATORS ON Rn;324
6.1.34;34. ESSENTIALLY SELF-ADJOINT PSEUDODIFFERENTIAL OPERATORS: II. ATOMIC SPECTRA;328
6.1.35;35. ESSENTIALLY SELF-ADJOINT PSEUDODIFFERENTIAL OPERATORS: III. HERMITIAN ELLIPTIC OPERATORS ON A COMPACT MANIFOLD;336
6.1.36;36. INVARIANT DIFFERENTIAL OPERATORS;351
6.1.37;37. DIFFERENTIAL PROPERTIES OF SPHERICAL FUNCTIONS;365
6.1.38;38. EXAMPLE: SPHERICAL HARMONICS;368
7;REFERENCES;374
8;INDEX;379