Treatise on Analysis

Treatise on Analysis

1st Edition - January 1, 1993

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  • Author: J. Dieudonné
  • eBook ISBN: 9781483266831

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Description

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.

Table of Contents


  • 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

Product details

  • No. of pages: 374
  • Language: English
  • Copyright: © Academic Press 1993
  • Published: January 1, 1993
  • Imprint: Academic Press
  • eBook ISBN: 9781483266831

About the Author

J. Dieudonné

About the Editors

H. Bass

A. Borel

Affiliations and Expertise

Institute for Advanced Study, Princeton, NJ

J. Moser

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