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020 _a9783540456582
_9978-3-540-45658-2
024 7 _a10.1007/b84019
_2doi
050 4 _aQA331-355
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKD
_2thema
082 0 4 _a515.9
_223
100 1 _aAng, Dang Dinh.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMoment Theory and Some Inverse Problems in Potential Theory and Heat Conduction
_h[electronic resource] /
_cby Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aX, 186 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1792
505 0 _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.
520 _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.
650 0 _aFunctions of complex variables.
650 0 _aPotential theory (Mathematics).
650 0 _aDifferential equations, partial.
650 0 _aIntegral Transforms.
650 0 _aIntegral equations.
650 0 _aOperator theory.
650 1 4 _aFunctions of a Complex Variable.
_0http://scigraph.springernature.com/things/product-market-codes/M12074
650 2 4 _aPotential Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12163
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aIntegral Transforms, Operational Calculus.
_0http://scigraph.springernature.com/things/product-market-codes/M12112
650 2 4 _aIntegral Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12090
650 2 4 _aOperator Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12139
700 1 _aGorenflo, Rudolf.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aLe, Vy Khoi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aTrong, Dang Duc.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662182925
776 0 8 _iPrinted edition:
_z9783540440062
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1792
856 4 0 _uhttps://doi.org/10.1007/b84019
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11151
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