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

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 inaccu...

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Bibliographic Details
Main Authors: Ang, Dang D, Gorenflo, Rudolf, Le, Vy K, Trong, Dang D
Format: Book
Language:English
Subjects:
Differential equations, partial
Functions of a Complex Variable
Functions of complex variables
Integral Equations
Integral Transforms
Integral Transforms, Operational Calculus
Mathematics
Mathematics and Statistics
Operator Theory
Partial Differential Equations
Potential Theory
Potential theory (Mathematics)
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Summary: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.
ISSN:0075-8434
1617-9692
DOI:10.1007/b84019