LEADER 04816nam 22008775 450 001 996466622703316 005 20200706003300.0 010 $a3-540-45658-9 024 7 $a10.1007/b84019 035 $a(CKB)1000000000233278 035 $a(SSID)ssj0000324983 035 $a(PQKBManifestationID)12079272 035 $a(PQKBTitleCode)TC0000324983 035 $a(PQKBWorkID)10321296 035 $a(PQKB)11498551 035 $a(DE-He213)978-3-540-45658-2 035 $a(MiAaPQ)EBC6286417 035 $a(MiAaPQ)EBC5591917 035 $a(Au-PeEL)EBL5591917 035 $a(OCoLC)1066191584 035 $a(PPN)155182218 035 $a(EXLCZ)991000000000233278 100 $a20121227d2002 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMoment Theory and Some Inverse Problems in Potential Theory and Heat Conduction$b[electronic resource] /$fby Dang D. Ang, Rudolf Gorenflo, Vy K. Le, Dang D. Trong 205 $a1st ed. 2002. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002. 215 $a1 online resource (X, 186 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1792 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-44006-2 327 $aIntroduction -- 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. 330 $aMoment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1792 606 $aFunctions of complex variables 606 $aPotential theory (Mathematics) 606 $aPartial differential equations 606 $aIntegral transforms 606 $aOperational calculus 606 $aIntegral equations 606 $aOperator theory 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aIntegral Transforms, Operational Calculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12112 606 $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 615 0$aFunctions of complex variables. 615 0$aPotential theory (Mathematics). 615 0$aPartial differential equations. 615 0$aIntegral transforms. 615 0$aOperational calculus. 615 0$aIntegral equations. 615 0$aOperator theory. 615 14$aFunctions of a Complex Variable. 615 24$aPotential Theory. 615 24$aPartial Differential Equations. 615 24$aIntegral Transforms, Operational Calculus. 615 24$aIntegral Equations. 615 24$aOperator Theory. 676 $a510 700 $aAng$b Dang D$4aut$4http://id.loc.gov/vocabulary/relators/aut$01063949 702 $aGorenflo$b Rudolf$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLe$b Vy K$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTrong$b Dang D$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466622703316 996 $aMoment Theory and Some Inverse Problems in Potential Theory and Heat Conduction$92535439 997 $aUNISA