Treatise on Analysis - 1st Edition - ISBN: 9780122155086, 9781483266831

Treatise on Analysis

1st Edition

Authors: J. Dieudonné
Editors: H. Bass A. Borel J. Moser
eBook ISBN: 9781483266831
Imprint: Academic Press
Published Date: 17th June 1993
Page Count: 374
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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 Operato

Details

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

About the Author

J. Dieudonné

About the Editor

H. Bass

A. Borel

Affiliations and Expertise

Institute for Advanced Study, Princeton, NJ

J. Moser

Ratings and Reviews