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

By: Ang, Dang Dinh [author.]Contributor(s): Gorenflo, Rudolf [author.] | Le, Vy Khoi [author.] | Trong, Dang Duc [author.] | SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Mathematics ; 1792Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2002Description: X, 186 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540456582Subject(s): Mathematics | Functions of complex variables | Integral equations | Integral Transforms | Operator theory | Differential equations, partial | Potential theory (Mathematics) | Mathematics | Functions of a Complex Variable | Potential Theory | Partial Differential Equations | Integral Transforms, Operational Calculus | Integral Equations | Operator TheoryAdditional physical formats: Printed edition:: No titleDDC classification: 515.9 LOC classification: QA331-355Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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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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.

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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