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 |

SUMMARY

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

CONTENT

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

Mathematics
Functions of complex variables
Integral equations
Integral transforms
Operational calculus
Operator theory
Partial differential equations
Potential theory (Mathematics)
Mathematics
Functions of a Complex Variable
Potential Theory
Partial Differential Equations
Integral Transforms Operational Calculus
Integral Equations
Operator Theory