ENGLISH

Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

By Rudolf Gorenflo , Dang Dinh Ang , Vy Khoi Le , Dang Duc Trong (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2002
ISBN
978-3-540-44006-2, 978-3-540-45658-2
DOI
10.1007/b84019
Language
english
Format
PDF
Filesize
2 MB (1858608 bytes)
Series
Lecture Notes in Mathematics 1792
Edition
1
Pages
186\177
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Functions of a Complex Variable; Potential Theory;Operational Calculus; Integral Equations; Operator

Description

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.

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