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# Treatise on Analysis

- 1st Edition - January 1, 1993
- Author: J. Dieudonné
- Editors: H. Bass, A. Borel, J. Moser
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 8 1 7 - 3
- Hardback ISBN:9 7 8 - 0 - 1 2 - 2 1 5 5 0 8 - 6
- 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 quote*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 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: January 1, 1993
- Imprint: Academic Press
- Paperback ISBN: 9781483238173
- Hardback ISBN: 9780122155086
- eBook ISBN: 9781483266831

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