TY - BOOK ID - 50230315 TI - Moment theory and some inverse problems in potential theory and heat conduction AU - Ang, Dang Dinh AU - Gorenflo, Rudolf AU - Khoi Le, Vy PY - 2002 VL - 1792 SN - 00758434 SN - 3540440062 3540456589 9783540440062 PB - Berlin: Springer, DB - UniCat KW - Moment problems (Mathematics) KW - Inverse problems (Differential equations) KW - Potential theory (Mathematics) KW - Heat KW - Conduction KW - Mathematical models KW - Functions of complex variables. KW - Potential theory (Mathematics). KW - Partial differential equations. KW - Integral transforms. KW - Operational calculus. KW - Integral equations. KW - Operator theory. KW - Functions of a Complex Variable. KW - Potential Theory. KW - Partial Differential Equations. KW - Integral Transforms, Operational Calculus. KW - Integral Equations. KW - Operator Theory. KW - Functional analysis KW - Equations, Integral KW - Functional equations KW - Operational calculus KW - Differential equations KW - Electric circuits KW - Integral equations KW - Transform calculus KW - Transformations (Mathematics) KW - Partial differential equations KW - Green's operators KW - Green's theorem KW - Potential functions (Mathematics) KW - Potential, Theory of KW - Mathematical analysis KW - Mechanics KW - Complex variables KW - Elliptic functions KW - Functions of real variables KW - Heat - Conduction - Mathematical models UR - https://www.unicat.be/uniCat?func=search&query=sysid:50230315 AB - 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. ER -