Geometric scattering theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1995
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Stanford lectures
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 116 S. graph. Darst. |
| ISBN: | 052149673X 0521498104 |
Internformat
MARC
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| 100 | 1 | |a Melrose, Richard B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometric scattering theory |c Richard B. Melrose |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XI, 116 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Stanford lectures | |
| 650 | 4 | |a Dispersion (Mathématiques) | |
| 650 | 7 | |a Dispersion (Mathématiques) |2 ram | |
| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Scattering (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804125079808770048 |
|---|---|
| adam_text | Contents
List of Illustrations page viii
Preface ix
Introduction xi
1 Euclidean Laplacian 1
1.1 The Laplacian 1
1.2 Spectral resolution 2
1.3 Scattering matrix 4
1.4 Resolvent family 6
1.5 Limiting absorption principle 7
1.6 Analytic continuation 9
1.7 Asymptotic expansion 11
1.8 Radial compactification 13
2 Potential scattering on R 15
2.1 The resolvent of A + V 15
2.2 Poles of the resolvent 18
2.3 Boundary pairing 19
2.4 Formal solutions 21
2.5 Unique continuation 21
2.6 Perturbed plane waves 22
2.7 Relative scattering matrix 22
2.8 Asymptotics of the resolvent 24
2.9 I? eigenfunctions 25
2.10 Zero energy states 25
2.11 Meromorphy of the scattering matrix 26
3 Inverse scattering 27
3.1 Radon transform 27
3.2 Wave group 30
3.3 Wave operators 33
v
vi Contents
3.4 Lax Phillips transform 33
3.5 Travelling waves 34
3.6 Near forward scattering 36
3.7 Constant energy inverse problem 37
3.8 Exponential solutions 39
3.9 Backscattering 40
4 Trace formulas and scattering poles 42
4.1 Determinant and scattering phase 43
4.2 Poisson formula 45
4.3 Existence of poles 46
4.4 Lax Phillips semigroup 47
4.5 Counting function 48
4.6 Pole free regions 51
5 Obstacle scattering 52
5.1 Obstacles 53
5.2 Scattering operator 55
5.3 Reflected geodesies 56
5.4 Ray relation 59
5.5 Trapped rays 62
6 Scattering metrics 65
6.1 Manifolds with boundary 66
6.2 Hodge theorem 67
6.3 Pseudodifferential operators 68
6.4 Symbol calculus 71
6.5 Index theorem 74
6.6 Limiting absorption principle 75
6.7 Generalized eigenfunctions 76
6.8 Scattering matrix 77
6.9 Long range potentials 79
6.10 Other theorems? 79
7 Cylindrical ends 80
7.1 b geometry 81
7.2 Thresholds 83
7.3 Scattering matrix 85
7.4 Boundary expansions and pairing 86
7.5 Hodge theory 87
7.6 Atiyah Patodi Singer index theorem 88
7.7 b Pseudodifferential operators 90
7.8 Trace formula and spectral asymptotics 91
7.9 Manifolds with corners 92
Contents vii
8 Hyperbolic metrics 94
8.1 Warped products 94
8.2 Conformally compact manifolds 96
8.3 0 geometry and analysis 98
8.4 The Laplacian 100
8.5 Analytic continuation 102
8.6 Finite volume quotients 103
8.7 hc geometry 103
8.8 Spectrum 104
References 106
Index 114
|
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| id | DE-604.BV010606212 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:55:52Z |
| institution | BVB |
| isbn | 052149673X 0521498104 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007075001 |
| oclc_num | 31865561 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-703 DE-384 DE-634 DE-11 DE-188 |
| physical | XI, 116 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Stanford lectures |
| spelling | Melrose, Richard B. Verfasser aut Geometric scattering theory Richard B. Melrose 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1995 XI, 116 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Stanford lectures Dispersion (Mathématiques) Dispersion (Mathématiques) ram Partiële differentiaalvergelijkingen gtt Scattering (Mathematics) Elliptischer Differentialoperator (DE-588)4140057-4 gnd rswk-swf Streuung Stochastik (DE-588)4183698-4 gnd rswk-swf Streuung Stochastik (DE-588)4183698-4 s DE-604 Elliptischer Differentialoperator (DE-588)4140057-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007075001&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Melrose, Richard B. Geometric scattering theory Dispersion (Mathématiques) Dispersion (Mathématiques) ram Partiële differentiaalvergelijkingen gtt Scattering (Mathematics) Elliptischer Differentialoperator (DE-588)4140057-4 gnd Streuung Stochastik (DE-588)4183698-4 gnd |
| subject_GND | (DE-588)4140057-4 (DE-588)4183698-4 |
| title | Geometric scattering theory |
| title_auth | Geometric scattering theory |
| title_exact_search | Geometric scattering theory |
| title_full | Geometric scattering theory Richard B. Melrose |
| title_fullStr | Geometric scattering theory Richard B. Melrose |
| title_full_unstemmed | Geometric scattering theory Richard B. Melrose |
| title_short | Geometric scattering theory |
| title_sort | geometric scattering theory |
| topic | Dispersion (Mathématiques) Dispersion (Mathématiques) ram Partiële differentiaalvergelijkingen gtt Scattering (Mathematics) Elliptischer Differentialoperator (DE-588)4140057-4 gnd Streuung Stochastik (DE-588)4183698-4 gnd |
| topic_facet | Dispersion (Mathématiques) Partiële differentiaalvergelijkingen Scattering (Mathematics) Elliptischer Differentialoperator Streuung Stochastik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007075001&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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