Integral geometry of tensor fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Utrecht
VSP
1994
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Inverse and ill-posed problems series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 271 S. graph. Darst. |
| ISBN: | 9067641650 |
Internformat
MARC
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| 100 | 1 | |a Šarafutdinov, Vladimir A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Integral geometry of tensor fields |c V. A. Sharafutdinov |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Utrecht |b VSP |c 1994 | |
| 300 | |a 271 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Inverse and ill-posed problems series | |
| 650 | 7 | |a Calcul tensoriel |2 ram | |
| 650 | 7 | |a Géométrie intégrale |2 ram | |
| 650 | 4 | |a Integral geometry | |
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Datensatz im Suchindex
| _version_ | 1804124527261646848 |
|---|---|
| adam_text | Contents
1 Introduction 11
1.1 The problem of determining a metric by its hodograph and a linearization
of the problem 11
1.2 The kinetic equation on a Riemannian manifold 14
1.3 Some remarks 17
2 The ray transform of symmetric tensor fields on Euclidean space 19
2.1 The ray transform and its relationship to the Fourier transform 20
2.2 Description of the kernel of the the ray transform in the smooth case ... 25
2.3 Equivalence of the first two statements of Theorem 2.2.1 in the case n = 2 26
2.4 Proof of Theorem 2.2.2 29
2.5 The ray transform of a field distribution 35
2.6 Decomposition of a tensor field into potential and solenoidal parts 38
2.7 A theorem on the tangent component 41
2.8 A theorem on conjugate tensor fields on the sphere 46
2.9 Primality of the ideal ( x 2,(x,y)) 50
2.10 Description of the image of the ray transform 50
2.11 Integral moments of the function // 54
2.12 Inversion formulas for the ray transform 56
2.13 Proof of Theorem 2.12.1 59
2.14 Inversion of the ray transform on the space of field distributions 64
2.15 The Plancherel formula for the ray transform 67
2.16 Application of the ray transform to an inverse problem of photoelasticity . 70
2.17 Further results 77
3 Some questions of tensor analysis 81
3.1 Tensor fields 81
3.2 Covariant differentiation 84
3.3 Symmetric tensor fields 88
3.4 Semibasic tensor fields 93
3.5 The horizontal covariant derivative 97
3.6 Formulas of Gauss Ostrogradskii type for vertical and horizontal derivatives 102
7
8 CONTENTS
4 The ray transform on a Riemannian manifold 113
4.1 Compact dissipative Riemannian manifolds 114
4.2 The ray transform on a CDRM 117
4.3 The problem of inverting the ray transform 119
4.4 Pestov s differential identity 122
4.5 Poincare s inequality for semibasic tensor fields 124
4.6 Reduction of Theorem 4.3.3 to an inverse problem for the kinetic equation 128
4.7 Proof of Theorem 4.3.3 132
4.8 Consequences for the nonlinear problem of determining a metric from its
hodograph 134
4.9 Bibliographical remarks 138
5 The transverse ray transform 141
5.1 Electromagnetic waves in quasi isotropic media 142
5.1.1 The Maxwell equations 142
5.1.2 The eiconal equation 143
5.1.3 The amplitude of an electromagnetic wave 145
5.1.4 Rytov s law 149
5.1.5 The Euclidean form of the Rytov law 151
5.1.6 The inverse problem 153
5.2 The transverse ray transform on a CDRM 155
5.3 Reduction of Theorem 5.2.2 to an inverse problem for the kinetic equation 157
5.4 Estimation of the summand related to the right hand side of the kinetic
equation 159
5.5 Estimation of the boundary integral and summands depending on curvature 164
5.6 Proof of Theorem 5.2.2 166
5.7 Decomposition of the operators An and A 168
5.8 Proof of Lemma 5.6.1 172
5.9 Final remarks 174
6 The truncated transverse ray transform 177
6.1 The polarization ellipse 177
6.2 The truncated transverse ray transform 182
6.3 Proof of Theorem 6.2.2 183
6.4 Decomposition of the operator Q^ 189
6.5 Proof of Lemma 6.3.1 195
6.6 Inversion of the truncated transverse ray transform on Euclidean space . . 201
7 The mixed ray transform 205
7.1 Elastic waves in quasi isotropic media 205
7.1.1 The equations of dynamic elasticity 205
7.1.2 The eiconal equation 206
7.1.3 The amplitude of a compression wave 208
7.1.4 The amplitude of a shear wave 210
CONTENTS 9
7.1.5 Rytov s law 212
7.1.6 The inverse problem for compression waves 213
7.1.7 The inverse problem for shear waves 214
7.2 The mixed ray transform 215
7.3 Proof of Theorem 7.2.2 218
7.4 The algebraic part of the proof 220
8 The exponential ray transform 227
8.1 Formulation of the main definitions and results 228
8.2 The modified horizontal derivative 22
8.3 Proof of Theorem 8.1.1 236
8.4 The volume of a simple compact Riemannian manifold 242
8.5 Determining a metric in a prescribed conformal class 246
8.6 Bibliographical remarks 256
Bibliography 257
Index 267
|
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| author_facet | Šarafutdinov, Vladimir A. |
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| author_sort | Šarafutdinov, Vladimir A. |
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| classification_rvk | SK 370 |
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010132442 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:47:05Z |
| institution | BVB |
| isbn | 9067641650 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006729679 |
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| owner_facet | DE-824 |
| physical | 271 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | VSP |
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| series2 | Inverse and ill-posed problems series |
| spelling | Šarafutdinov, Vladimir A. Verfasser aut Integral geometry of tensor fields V. A. Sharafutdinov 1. publ. Utrecht VSP 1994 271 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Inverse and ill-posed problems series Calcul tensoriel ram Géométrie intégrale ram Integral geometry HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006729679&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Šarafutdinov, Vladimir A. Integral geometry of tensor fields Calcul tensoriel ram Géométrie intégrale ram Integral geometry |
| title | Integral geometry of tensor fields |
| title_auth | Integral geometry of tensor fields |
| title_exact_search | Integral geometry of tensor fields |
| title_full | Integral geometry of tensor fields V. A. Sharafutdinov |
| title_fullStr | Integral geometry of tensor fields V. A. Sharafutdinov |
| title_full_unstemmed | Integral geometry of tensor fields V. A. Sharafutdinov |
| title_short | Integral geometry of tensor fields |
| title_sort | integral geometry of tensor fields |
| topic | Calcul tensoriel ram Géométrie intégrale ram Integral geometry |
| topic_facet | Calcul tensoriel Géométrie intégrale Integral geometry |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006729679&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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