An Introduction to inverse scattering and inverse spectral problems:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Philadelphia, PA
SIAM
1997
|
| Series: | SIAM monographs on mathematical modeling and computation
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 198 S. |
| ISBN: | 0898713870 |
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MARC
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Record in the Search Index
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Contents
Foreword vii
Preface ix
1. A Review of Basic Mathematical Tools 1
Lassi Pdivdrinta
1.1 Linear Operators on Hilbert Space 1
1.2 Integral Operators and the Predholm Alternative 2
1.3 The Fourier Transform and the Hilbert Transform 5
1.4 The Unique Continuation Principle (UCP) 7
1.5 Unbounded Operators 7
1.6 The Spectrum 9
1.7 The Resolvent Kernel and the Fredholm Determinant 11
1.8 A Particle in a Box 15
1.9 Maxwell's Equations 18
References 24
2. Multidimensional Inverse Scattering Theory 25
David Colton
2.1 Electromagnetic Scattering Problem 25
2.2 Bessel Functions 28
2.3 The Addition Formula 30
2.4 Green's Formula 32
2.5 Basic Properties of Far Field Patterns 37
2.6 Spectral Theory of the Far Field Operator 41
2.7 The Inverse Scattering Problem 45
2.8 The Detection and Monitoring of Leukemia 54
2.9 Regularization 62
2.10 Closing Remarks 65
v
vi Contents
References 66
3. Inverse Sturm Liouville Problems 67
William Rundell
3.0 Introduction 67
3.1 Preliminary Material 70
3.2 The Liouville Transformation 76
3.3 Asymptotic Expansions of the Eigenvalues and Eigenfunctions . 77
3.4 The Inverse Problem—A Historical Look 83
3.5 A Completeness Result 85
3.6 An Important Integral Operator 86
3.7 Solving Hyperbolic Equations 90
3.8 Uniqueness Proofs 91
3.9 Constructive Algorithms 94
3.10 Modification for Other Spectral Data 102
3.11 Other Differential Equations 108
3.12 Other Constructive Algorithms 113
3.13 The Matrix Analogue 114
3.14 Another Finite Dimensional Algorithm 117
3.15 Fourth Order Problems 123
References 125
4. Inverse Problems in Potential Scattering 131
Khosrow Chadan
4.1 Introduction 131
4.2 Physical Background and Formulation of the Inverse Scattering
Problem 131
4.3 Scattering Theory for Partial Waves 137
4.4 Gel'fand Levitan Integral Equation 164
4.5 Marchenko Equation 174
4.6 Inverse Problem on the Line 178
4.7 Nonlinear Evolution Equations 186
4.8 Closing Remarks 190
A Appendix 190
References 191
Index 195 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011577428 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-05T13:01:21Z |
| institution | BVB |
| isbn | 0898713870 |
| language | English |
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| physical | VIII, 198 S. |
| publishDate | 1997 |
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| publisher | SIAM |
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| series2 | SIAM monographs on mathematical modeling and computation |
| spelling | An Introduction to inverse scattering and inverse spectral problems Khosrow Chadan ... Philadelphia, PA SIAM 1997 VIII, 198 S. txt rdacontent n rdamedia nc rdacarrier SIAM monographs on mathematical modeling and computation Inverse Spektraltheorie (DE-588)4314037-3 gnd rswk-swf Inverse Spektraltheorie (DE-588)4314037-3 s DE-604 Chadan, Khosrow Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007796367&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | An Introduction to inverse scattering and inverse spectral problems Inverse Spektraltheorie (DE-588)4314037-3 gnd |
| subject_GND | (DE-588)4314037-3 |
| title | An Introduction to inverse scattering and inverse spectral problems |
| title_auth | An Introduction to inverse scattering and inverse spectral problems |
| title_exact_search | An Introduction to inverse scattering and inverse spectral problems |
| title_full | An Introduction to inverse scattering and inverse spectral problems Khosrow Chadan ... |
| title_fullStr | An Introduction to inverse scattering and inverse spectral problems Khosrow Chadan ... |
| title_full_unstemmed | An Introduction to inverse scattering and inverse spectral problems Khosrow Chadan ... |
| title_short | An Introduction to inverse scattering and inverse spectral problems |
| title_sort | an introduction to inverse scattering and inverse spectral problems |
| topic | Inverse Spektraltheorie (DE-588)4314037-3 gnd |
| topic_facet | Inverse Spektraltheorie |
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