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Treatise on Analysis
- 1st Edition - June 3, 2016
- Author: J. Dieudonné
- Editors: H. Bass, A. Borel, J. Moser
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 6 8 3 - 1
Treatise on Analysis, Volume 10–VIII provides information pertinent to the study of the most common boundary problems for partial differential equations. This book presents… Read more
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Request a sales quoteTreatise on Analysis, Volume 10–VIII provides information pertinent to the study of the most common boundary problems for partial differential equations. This book presents the study of Cauchy's problem in its most elementary form.
Comprised of one chapter, this volume begins with an overview of Hilbert-von Neumann spectral theory and explores all possible boundary conditions related to spectral theory. This text then examines the link of Cauchy's problem with the behavior of the equation's characteristics. This book discusses as well the case of linear elliptic operators. The reader is also introduced to Sobolev spaces and some of their generalizations that provide an essential tool in the study of these elliptic problems, and their manipulation requires delicate upper bounds to obtain the best possible results.
This book is a valuable resource for mathematicians.
Notation
Chapter XXIII Linear Functional Equations
Part II.: Boundary Value Problems
39. Weyl-Kodaira Theory: I. Elliptic Differential Operators on an Interval of R
40. Weyl-Kodaira Theory: II. Boundary Conditions
41. Weyl-Kodaira Theory: III. Self-Adjoint Operators Associated with a Linear Differential Equation
42. Weyl-Kodaira Theory: IV. Green Function and Spectrum
43. Weyl-Kodaira Theory: V. The Case of Second Order Equations
44. Weyl-Kodaira Theory: VI. Example: Second Order Equations with Periodic Coefficients
45. Weyl-Kodaira Theory: VII. Example: Gelfand-Levitan Equations
46. Multilayer Potentials: I. Symbols of Rational Type
47. Multilayer Potentials: II. The Case of Hyperplane Multilayers
48. Multilayer Potentials: III. General Case
49. Fine Boundary Value Problems for Elliptic Differential Operators: I. The Calderon Operator
50. Fine Boundary Value Problems for Elliptic Differential Operators: II. Elliptic Boundary Value Problems
51. Fine Boundary Value Problems for Elliptic Differential Operators: III. Ellipticity Criteria
52. Fine Boundary Value Problems for Elliptic Differential Operators: IV. The Spaces Hs,r(U+)
53. Fine Boundary Value Problems for Elliptic Differential Operators: V. Hs,r-Spaces and P-Potentials
54. Fine Boundary Value Problems for Elliptic Differential Operators: VI. Regularity on the Boundary
55. Fine Boundary Value Problems for Elliptic Differential Operators: VII. Coercive Problems
56. Fine Boundary Value Problems for Elliptic Differential Operators: VIII. Generalized Green's Formula
57. Fine Boundary Value Problems for Elliptic Differential Operators: IX. Fine Problems Associated with Coercive Problems
58. Fine Boundary Value Problems for Elliptic Differential Operators: X. Examples
59. Fine Boundary Value Problems for Elliptic Differential Operators: XI. Extension to some Non-Hermitian Operators
60. Fine Boundary Value Problems for Elliptic Differential Operators: XII. Case of Second-Order Operators; Neumann's Problem
61. Fine Boundary Value Problems for Elliptic Differential Operators: XIII. The Maximum Principle
62. Parabolic Equations: I. Construction of a One-Sided Local Resolvent
63. Parabolic Equations: II. The One-Sided Global Cauchy Problem
64. Parabolic Equations: III. Traces and Eigenvalues
65. Evolution Distributions
66. The Wave Equation: I. Generalized Cauchy Problem
67. The Wave Equation: II. Propagation and Domain of Influence
68. The Wave Equation: III. Signals, Waves, and Rays
69. Strictly Hyperbolic Equations: I. Preliminary Results
70. Strictly Hyperbolic Equations: II. Construction of a Local Approximate Resolvent
71. Strictly Hyperbolic Equations: III. Examples and Variations
72. Strictly Hyperbolic Equations: IV. The Cauchy Problem for Strictly Hyperbolic Differential Operators; Existence and Local Uniqueness
73. Strictly Hyperbolic Equations: V. Global Problems
74. Strictly Hyperbolic Equations: VI. Extension to Manifolds
75. Application to the Spectrum of a Hermitian Elliptic Operator
References
Index
- No. of pages: 374
- Language: English
- Edition: 1
- Published: June 3, 2016
- Imprint: Academic Press
- eBook ISBN: 9781483266831
AB
A. Borel
Affiliations and expertise
Institute for Advanced Study, Princeton, NJ