An introduction to linear and nonlinear scattering theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex, England
Longman
1995
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
78 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 254 S. |
| ISBN: | 0582092302 |
Staff View
MARC
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| 245 | 1 | 0 | |a An introduction to linear and nonlinear scattering theory |c G. F. Roach |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex, England |b Longman |c 1995 | |
| 300 | |a X, 254 S. | ||
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Record in the Search Index
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| adam_text | Contents
Preface ix
Chapter 1: Introduction and outline of contents 1
Chapter 2: Analytical preliminaries 11
2.1 Introduction 11
2.2 Preliminaries 11
2.3 Distribution theory 20
2.4 Hilbert space 35
2.5 Bounded linear operators on Hilbert spaces 41
2.6 Unbounded linear operators on Hilbert spaces 51
2.7 Adjoints of unbounded operators 57
2.8 A basic criterion for self adjointness 60
Chapter 3: Examples of scattering theory strategies 65
3.1 Introduction 65
3.2 A free problem 69
3.3 Properties of the operators Ag and Uo(t) 71
3.4 A perturbed problem 75
3.5 Comparison of solutions 77
3.6 Summary 80
Chapter 4: Elements of spectral theory 82
4.1 Introduction 82
4.2 Basic concepts 82
4.3 Eigenvalues and eigenvectors 85
vi Contents
4.4 Spectral decompositions on finite dimensional spaces 92
4.5 Spectral decomposition on infinite dimensional spaces 98
4.6 Properties of spectral families 101
4.7 Functions of an operator 108
4.8 Spectral decompositions of H 111
4.9 Examples 123
4.10 More on spectral decompositions associated with an operator 140
4.11 On the determination of spectral families 146
Chapter 5: Some applications of semigroup theory 152
5.1 Introduction and basic results 152
5.2 On the well posedness of problems 158
5.3 Generators of semigroups 161
5.4 Perturbation of semigroups 167
Chapter 6: More about wave operators 169
6.1 Introduction 169
6.2 Abstract evolutionary systems 169
6.3 The scattering operator 171
6.4 Existence of wave operators 174
6.5 Selected properties of wave operators 176
6.6 On the completeness of wave operators 181
Chapter 7: Target scattering 183
7.1 Introduction 183
7.2 Concerning the incident field 183
7.3 A typical target scattering problem 185
7.4 Solution concepts 191
7.5 Concerning existence and uniqueness of solutions 194
Contents vii
Chapter 8: A scattering theory 201
8.1 Introduction 201
8.2 A free problem 202
8.3 A perturbed problem 209
8.4 Concerning the wave operators 216
8.5 Summary and additional comments 218
Chapter 9: Nonlinear scattering theory 222
9.1 Introduction 222
9.2 Concerning existence of solutions 225
9.3 Scattering theory 227
9.4 More on conditions ensuring scattering 236
Chapter 10: Commentaries 240
References 246
Index 252
|
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| callnumber-subject | QA - Mathematics |
| classification_tum | MAT 358f MAT 418f |
| ctrlnum | (OCoLC)246506453 (DE-599)BVBBV010652069 |
| dewey-full | 515/.724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.724 |
| dewey-search | 515/.724 |
| dewey-sort | 3515 3724 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010652069 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:56:39Z |
| institution | BVB |
| isbn | 0582092302 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007109178 |
| oclc_num | 246506453 |
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| owner_facet | DE-12 DE-91 DE-BY-TUM DE-706 DE-83 DE-11 |
| physical | X, 254 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Longman |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Roach, Gary F. 1933- Verfasser (DE-588)137433077 aut An introduction to linear and nonlinear scattering theory G. F. Roach 1. publ. Harlow, Essex, England Longman 1995 X, 254 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 78 Dispersion (Mathématiques) ram Théories non linéaires ram Nonlinear theories Scattering (Mathematics) Streutheorie (DE-588)4183697-2 gnd rswk-swf Streuung Stochastik (DE-588)4183698-4 gnd rswk-swf Streuung Stochastik (DE-588)4183698-4 s DE-604 Streutheorie (DE-588)4183697-2 s Pitman monographs and surveys in pure and applied mathematics 78 (DE-604)BV000022446 78 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007109178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roach, Gary F. 1933- An introduction to linear and nonlinear scattering theory Pitman monographs and surveys in pure and applied mathematics Dispersion (Mathématiques) ram Théories non linéaires ram Nonlinear theories Scattering (Mathematics) Streutheorie (DE-588)4183697-2 gnd Streuung Stochastik (DE-588)4183698-4 gnd |
| subject_GND | (DE-588)4183697-2 (DE-588)4183698-4 |
| title | An introduction to linear and nonlinear scattering theory |
| title_auth | An introduction to linear and nonlinear scattering theory |
| title_exact_search | An introduction to linear and nonlinear scattering theory |
| title_full | An introduction to linear and nonlinear scattering theory G. F. Roach |
| title_fullStr | An introduction to linear and nonlinear scattering theory G. F. Roach |
| title_full_unstemmed | An introduction to linear and nonlinear scattering theory G. F. Roach |
| title_short | An introduction to linear and nonlinear scattering theory |
| title_sort | an introduction to linear and nonlinear scattering theory |
| topic | Dispersion (Mathématiques) ram Théories non linéaires ram Nonlinear theories Scattering (Mathematics) Streutheorie (DE-588)4183697-2 gnd Streuung Stochastik (DE-588)4183698-4 gnd |
| topic_facet | Dispersion (Mathématiques) Théories non linéaires Nonlinear theories Scattering (Mathematics) Streutheorie Streuung Stochastik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007109178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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