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

• Main Authors: Ang, Dang D. (Author, http://id.loc.gov/vocabulary/relators/aut), Gorenflo, Rudolf (http://id.loc.gov/vocabulary/relators/aut), Le, Vy K. (http://id.loc.gov/vocabulary/relators/aut), Trong, Dang D. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1792
• Subjects: Functions of complex variables.; Potential theory (Mathematics).; Partial differential equations.; Integral transforms.; Operational calculus.; Integral equations.; Operator theory.; Functions of a Complex Variable.; Potential Theory.; Partial Differential Equations.; Integral Transforms, Operational Calculus.; Integral Equations.; Operator Theory.

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 inaccu...

Table of 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.