By L. H. Reiss
Publisher: Gulf Pub Co
Number Of Pages:
Publication Date: 1981-01
ISBN-10/ ASIN: 0872013030
ISBN-13/ EAN: 9780872013032
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Friday, February 13, 2009
Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction (Lecture Notes in Mathematics)
by Walter J. Greiner D. D. Ang R. Gorenflo
Table of Contents
Introduction
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 54
3.3 Regularization via Backus-Gilbert solutions 63
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 131
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
- References
- Index
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Table of Contents
Introduction
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 54
3.3 Regularization via Backus-Gilbert solutions 63
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 131
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
- References
- Index
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