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Moment theory and some inverse problems in potential theory and heat conduction [electronic resource] / Dang Dinh Ang [and others].

Published
Berlin ; New York : Springer, [2002]
Copyright Date
©2002
Physical Description
viii, 183 pages ; 24 cm.
Additional Creators
Ang, Dang Dinh, 1928-
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Contents
Machine generated contents note: 1.Mathematical preliminaries -- 1.1.Banach spaces -- 1.2.Hilbert spaces -- 1.3.Some useful function spaces -- 1.4.Analytic functions and harmonic functions -- 1.5.Fourier transform and Laplace transform -- 2.Regularization of moment problems by truncated expansion and by the Tikhonov method -- 2.1.Method of truncated expansion -- 2.2.Method of Tikhonov -- 2.3.Notes and remarks -- 3.Backus-Gilbert regularization of a moment problem -- 3.1.Introduction -- 3.2.Backus-Gilbert solutions and their stability -- 3.3.Regularization via Backus-Gilbert solutions -- 4.The Hausdorff moment problem: regularization and error estimates -- 4.1.Finite moment approximation of (4.1) -- 4.2.A moment problem from Laplace transform -- 4.3.Notes and remarks -- 5.Analytic functions: reconstruction and Sinc approximations -- 5.1.Reconstruction of functions in H[superscript 2](U): approximation by polynomials -- 5.2.Reconstruction of an analytic function: a problem of optimal recovery -- 5.3.Cardinal series representation and approximation: reformulation of moment problems -- 6.Regularization of some inverse problems in potential theory -- 6.1.Analyticity of harmonic functions -- 6.2.Cauchy's problem for the Laplace equation -- 6.3.Surface temperature determination from borehole measurements (steady case) -- 7.Regularization of some inverse problems in heat conduction -- 7.1.The backward heat equation -- 7.2.Surface temperature determination from borehole measurements: a two-dimensional problem -- 7.3.An inverse two-dimensional Stefan problem: identification of boundary values -- 7.4.Notes and remarks -- 8.Epilogue.
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ISBN
3540440062 (acid-free paper)
Bibliography Note
Includes bibliographical references (pages [175]-180) and index.
View MARC record | catkey: 7861511