Author	Ang, Dang Dinh. author
Title	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
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2002
Connect to	http://dx.doi.org/10.1007/b84019
Descript	X, 186 p. online resource

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

1. Mathematics
2. Functions of complex variables
3. Integral equations
4. Integral transforms
5. Operational calculus
6. Operator theory
7. Partial differential equations
8. Potential theory (Mathematics)
9. Mathematics
10. Functions of a Complex Variable
11. Potential Theory
12. Partial Differential Equations
13. Integral Transforms
14. Operational Calculus
15. Integral Equations
16. Operator Theory