Geometric scattering theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Edition: | transferred to digital print. |
| Series: | Stanford lectures
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 116 S. graph. Darst. |
| ISBN: | 052149673X 0521498104 |
Staff View
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 |
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Record in the Search Index
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|---|---|
| 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
б
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 Rn
15
2.1
The resolvent of
Δ
+
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 1?
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
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 formulae 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
8
Hyperbolic metrics
8.1
Warped products
8.2
Conformally compact manifolds
8.3
О
-geometry
and analysis
8.4
The Laplacian
8.5
Analytic continuation
8.6
Finite volume quotients
8.7
hc-geometry
8.8
Spectrum
References
Index
Contents
vii
94
94
96
98
100
102
103
103
104
106
114
|
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| discipline | Mathematik |
| edition | transferred to digital print. |
| format | Book |
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| id | DE-604.BV035309921 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:58Z |
| institution | BVB |
| isbn | 052149673X 0521498104 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017114681 |
| oclc_num | 249349863 |
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| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XI, 116 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Stanford lectures |
| spelling | Melrose, Richard B. Verfasser aut Geometric scattering theory Richard B. Melrose transferred to digital print. Cambridge [u.a.] Cambridge Univ. Press 2003 XI, 116 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Stanford lectures 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017114681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Melrose, Richard B. Geometric scattering theory 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 | Elliptischer Differentialoperator (DE-588)4140057-4 gnd Streuung Stochastik (DE-588)4183698-4 gnd |
| topic_facet | Elliptischer Differentialoperator Streuung Stochastik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017114681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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