Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

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File Name: Ang, Gorenflo, Le, Trong. Moment theory, inverse problems in potential theory and heat conduction (LNM1792,Springer,2002)(ISBN 3540440062)(185s).pdf
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Volume info:
Series: Lecture Notes in Mathematics 1792
Periodical:
Author: Dang Dinh Ang,Rudolf Gorenflo,Vy Khoi Le,Dang Duc Trong (auth.)
Year: 2002
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
City:
Pages: 186
PagesInFile: 185
Language: English
Topic: Mathematics > Analysis
Library: Kolxo3
Library issue: 14

Commentary:
DPI: 0
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Paginated:
Scanned: 1
Bookmarked:
Searchable: 1

Identifiers:

ISBN: 3540440062,9783540440062
ISSN:
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UDC:
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DDC:
LCC:
DOI: 10.1007/b84019
Googlebook id:
Openlibrary id: OL9057863M

CRC32: EA874735
SHA1: JQ5TO4KZEJYIUQHXNBYQVUH773H36TN6
SHA256: 956A636D6D64F8AFB6FAC9CFF772F008FD73BDF3D6091ACC6E7DB3ECAA623DAF
MD5: 5C65EE32334A7D050B5093A88C2B8FB6

TOC:

Introduction....Pages 1-3
1. Mathematical preliminaries....Pages 5-16
2. Regularization of moment problems by truncated expansion and by the Tikhonov method....Pages 17-49
3. Backus-Gilbert regularization of a moment problem....Pages 51-81
4. The Hausdorff moment problem: regularization and error estimates....Pages 83-97
5. Analytic functions: reconstruction and Sinc approximations....Pages 99-130
6. Regularization of some inverse problems in potential theory....Pages 131-146
7. Regularization of some inverse problems in heat conduction....Pages 147-169
8. Epilogue....Pages 171-173
References....Pages 175-180
Index....Pages 181-183

Description:

Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations.

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