04816nam 22008775 450 99646662270331620200706003300.03-540-45658-910.1007/b84019(CKB)1000000000233278(SSID)ssj0000324983(PQKBManifestationID)12079272(PQKBTitleCode)TC0000324983(PQKBWorkID)10321296(PQKB)11498551(DE-He213)978-3-540-45658-2(MiAaPQ)EBC6286417(MiAaPQ)EBC5591917(Au-PeEL)EBL5591917(OCoLC)1066191584(PPN)155182218(EXLCZ)99100000000023327820121227d2002 u| 0engurnn|008mamaatxtccrMoment Theory and Some Inverse Problems in Potential Theory and Heat Conduction[electronic resource] /by Dang D. Ang, Rudolf Gorenflo, Vy K. Le, Dang D. Trong1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (X, 186 p.) Lecture Notes in Mathematics,0075-8434 ;1792Bibliographic Level Mode of Issuance: Monograph3-540-44006-2 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.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.Lecture Notes in Mathematics,0075-8434 ;1792Functions of complex variablesPotential theory (Mathematics)Partial differential equationsIntegral transformsOperational calculusIntegral equationsOperator theoryFunctions of a Complex Variablehttps://scigraph.springernature.com/ontologies/product-market-codes/M12074Potential Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12163Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Integral Transforms, Operational Calculushttps://scigraph.springernature.com/ontologies/product-market-codes/M12112Integral Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12090Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Functions of complex variables.Potential theory (Mathematics).Partial differential equations.Integral transforms.Operational calculus.Integral equations.Operator theory.Functions of a Complex Variable.Potential Theory.Partial Differential Equations.Integral Transforms, Operational Calculus.Integral Equations.Operator Theory.510Ang Dang Dauthttp://id.loc.gov/vocabulary/relators/aut1063949Gorenflo Rudolfauthttp://id.loc.gov/vocabulary/relators/autLe Vy Kauthttp://id.loc.gov/vocabulary/relators/autTrong Dang Dauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK996466622703316Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction2535439UNISA