Moment theory and some inverse problems in potential theory and heat conduction:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Lecture notes in mathematics
1792 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 183 S. |
| ISBN: | 3540440062 |
Staff View
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| 245 | 1 | 0 | |a Moment theory and some inverse problems in potential theory and heat conduction |c Dang Dinh Ang ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a VIII, 183 S. | ||
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Record in the Search Index
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| adam_text | Table of Contents
Introduction 1
1 Mathematical preliminaries 5
1.1 Banach spaces 5
1.2 Hilbert spaces 6
1.3 Some useful function spaces 8
1.3.1 Spaces of continuous functions 8
1.3.2 Spaces of integrable functions 9
1.3.3 Sobolev spaces 10
1.4 Analytic functions and harmonic functions 12
1.5 Fourier transform and Laplace transform 14
2 Regularization of moment problems by truncated expansion
and by the Tikhonov method 17
2.1 Method of truncated expansion 19
2.1.1 A construction of regularized solutions 19
2.1.2 Convergence of regularized solutions and error estimates ... 22
2.1.3 Error estimates using eigenvalues of the Laplacian 27
2.2 Method of Tikhonov 30
2.2.1 Case 1: exact solutions in L2{f2) 30
2.2.2 Case 2: exact solutions in La~ (/?), 1 q* oo 36
2.2.3 Case 3: exact solutions in Hl (_ ?) 42
2.3 Notes and remarks 45
3 Backus Gilbert regularization of a moment problem 51
3.1 Introduction 51
3.2 Backus Gilbert solutions and their stability 54
3.2.1 Definition of the Backus Gilbert solutions 54
3.2.2 Stability of the Backus Gilbert solutions 59
3.3 Regularization via Backus Gilbert solutions 63
3.3.1 Definitions and notations fi4
3.3.2 Main results 73
4 The Hausdorff moment problem: regularization and error
estimates 83
4.1 Finite moment approximation of (4.1) 84
4.1.1 Proof of Theorem 4.1 88
viii Table of Contents
4.1.2 Proof of Theorem 4.2 89
4.2 A moment problem from Laplace transform 92
4.3 Notes and remarks 94
5 Analytic functions: reconstruction and Sine approximations.... 99
5.1 Reconstruction of functions in H2(U): approximation by polynomials 99
5.2 Reconstruction of an analytic function: a problem of optimal
recovery 106
5.3 Cardinal series representation and approximation: reformulation
of moment problems 120
5.3.1 Two dimensional Sine theory 120
5.3.2 Approximation theorems 123
6 Regularization of some inverse problems in potential theory . .. 131
6.1 Analyticity of harmonic functions 131
6.2 Cauchy s problem for the Laplace equation 133
6.3 Surface temperature determination from borehole measurements
(steady case) 145
7 Regularization of some inverse problems in heat conduction . .. 147
7.1 The backward heat equation 147
7.2 Surface temperature determination from borehole measurements:
a two dimensional problem 155
7.3 An inverse two dimensional Stefan problem: identification of
boundary values 164
7.4 Notes and remarks 169
8 Epilogue 171
References 175
Index 181
|
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| indexdate | 2024-07-09T19:04:16Z |
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| isbn | 3540440062 |
| language | English |
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| physical | VIII, 183 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Moment theory and some inverse problems in potential theory and heat conduction Dang Dinh Ang ... Berlin [u.a.] Springer 2002 VIII, 183 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1792 Wärmeleitungsgleichung (DE-588)4188859-5 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Moment Mathematik (DE-588)4330407-2 gnd rswk-swf Momentenmethode Mathematik (DE-588)4320678-5 gnd rswk-swf Moment Mathematik (DE-588)4330407-2 s Inverses Problem (DE-588)4125161-1 s Potenzialtheorie (DE-588)4046939-6 s DE-604 Momentenmethode Mathematik (DE-588)4320678-5 s Wärmeleitungsgleichung (DE-588)4188859-5 s Ang, Dang-Dinh Sonstige oth Lecture notes in mathematics 1792 (DE-604)BV000676446 1792 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009928769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moment theory and some inverse problems in potential theory and heat conduction Lecture notes in mathematics Wärmeleitungsgleichung (DE-588)4188859-5 gnd Potenzialtheorie (DE-588)4046939-6 gnd Inverses Problem (DE-588)4125161-1 gnd Moment Mathematik (DE-588)4330407-2 gnd Momentenmethode Mathematik (DE-588)4320678-5 gnd |
| subject_GND | (DE-588)4188859-5 (DE-588)4046939-6 (DE-588)4125161-1 (DE-588)4330407-2 (DE-588)4320678-5 |
| title | Moment theory and some inverse problems in potential theory and heat conduction |
| title_auth | Moment theory and some inverse problems in potential theory and heat conduction |
| title_exact_search | Moment theory and some inverse problems in potential theory and heat conduction |
| title_full | Moment theory and some inverse problems in potential theory and heat conduction Dang Dinh Ang ... |
| title_fullStr | Moment theory and some inverse problems in potential theory and heat conduction Dang Dinh Ang ... |
| title_full_unstemmed | Moment theory and some inverse problems in potential theory and heat conduction Dang Dinh Ang ... |
| title_short | Moment theory and some inverse problems in potential theory and heat conduction |
| title_sort | moment theory and some inverse problems in potential theory and heat conduction |
| topic | Wärmeleitungsgleichung (DE-588)4188859-5 gnd Potenzialtheorie (DE-588)4046939-6 gnd Inverses Problem (DE-588)4125161-1 gnd Moment Mathematik (DE-588)4330407-2 gnd Momentenmethode Mathematik (DE-588)4320678-5 gnd |
| topic_facet | Wärmeleitungsgleichung Potenzialtheorie Inverses Problem Moment Mathematik Momentenmethode Mathematik |
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