Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction / by Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong.

Format:

Book

Author/Creator:

Ang, Dang Dinh, 1928- author.

Gorenflo, Rudolf, author.

Le, Vy Khoi, author.

Trong, Dang Duc, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1792.

Lecture Notes in Mathematics, 0075-8434 ; 1792

Language:

English

Subjects (All):

Functions of complex variables.

Potential theory (Mathematics).

Differential equations, Partial.

Integral transforms.

Integral equations.

Operator theory.

Functions of a Complex Variable.

Potential Theory.

Partial Differential Equations.

Integral Transforms, Operational Calculus.

Integral Equations.

Operator Theory.

Local Subjects:

Functions of a Complex Variable.

Potential Theory.

Partial Differential Equations.

Integral Transforms, Operational Calculus.

Integral Equations.

Operator Theory.

Physical Description:

1 online resource (X, 186 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.

System Details:

text file PDF

Summary:

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.

Contents:

Introduction

Mathematical Preliminaries

Regularization of moment problems by trancated expansion and by the Tikhonov method

Backus-Gilbert regularization of a moment problem

The Hausdorff moment problem: regularization and error estimates

Analytic functions: reconstruction and Sinc approximations

Regularization of some inverse problems in potential theory

Regularization of some inverse problems in heat conduction

Epilogue

References

Index.

Other Format:

Printed edition:

ISBN:

9783540456582

Access Restriction:

Restricted for use by site license.