Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong (auth.)3540440062, 9783540440062
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. |
Table of contents :
Introduction….Pages 1-3
1. Mathematical preliminaries….Pages 5-16
2. Regularization of moment problems by truncated expansion and by the Tikhonov method….Pages 17-49
3. Backus-Gilbert regularization of a moment problem….Pages 51-81
4. The Hausdorff moment problem: regularization and error estimates….Pages 83-97
5. Analytic functions: reconstruction and Sinc approximations….Pages 99-130
6. Regularization of some inverse problems in potential theory….Pages 131-146
7. Regularization of some inverse problems in heat conduction….Pages 147-169
8. Epilogue….Pages 171-173
References….Pages 175-180
Index….Pages 181-183 |
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