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

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.

List 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.

Product details

• Authors: Dang D. Ang, Rudolf Gorenflo, Vy K. Le, Dang D. Trong
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 04.09.2002
• EAN: 9783540440062
• ISBN: 978-3-540-44006-2
• No. of pages: 186
• Dimensions: 157 mm x 236 mm x 13 mm
• Weight: 332 g
• Illustrations: X, 186 p.
• Series: Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Mathematics and Statistics, Partial Differential Equations, Differential calculus & equations, Differential equations, Stochastics, Operational calculus, Integral transforms, Integral Transforms and Operational Calculus, Integral Transforms, Operational Calculus, Integral calculus & equations, Integral Equations, Functional analysis & transforms, Operator Theory, Functions of a Complex Variable, Functions of complex variables, Potential Theory, Potential theory (Mathematics)