Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction: 1792 - Brossura

Le, Vy K.; Ang, Dang D.; Gorenflo, Rudolf; Trong, Dang D.

Brossura

ISBN 10: 3540440062 ISBN 13: 9783540440062

Casa editrice: Springer, 2008

Riassunto

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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Contenuti

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 Description

Book by Ang Dang D Gorenflo Rudolf Le Vy K Trong Dang D

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 3540440062
• ISBN 13: 9783540440062
• Rilegatura: Copertina flessibile
• Numero di pagine: 196
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania