Moment Theory And Some Inverse Problems In Potential Theory And Heat Conduction (lecture Notes In Mathematics)

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. 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. Dang Dinh Ang ... [et Al.]. Includes Bibliographical References (p. [175]-180) And Index. Also Available In An Electronic Version. 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