Multiparameter eigenvalue problems and expansion theorems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1988
|
| Schriftenreihe: | Lecture notes in mathematics
1356 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 157 S. |
| ISBN: | 3540504796 0387504796 |
Internformat
MARC
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| 100 | 1 | |a Volkmer, Hans |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multiparameter eigenvalue problems and expansion theorems |c Hans Volkmer |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1988 | |
| 300 | |a VI, 157 S. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1356 | |
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Datensatz im Suchindex
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| adam_text | CONTENTS
Introduction 1
CHAPTER 1 : Mul tiparameter eigenvalue problems for Hermitian matrices 8
1.1 Introduction 8
1.2 Indexed eigenvalues 9
1.3 The degree of a map 12
1.4 Existence of eigenvalues 13
1.5 Definite eigenvalue problems 17
1.6 Notes for Chapter 1 20
CHAPTER 2 : Mul ti parameter eigenvalue problems for bounded operators 21
2.1 Introduction 21
2.2 Some simple properties of eigenvalues 22
2.3 The joint range of forms 26
2.4 A boundedness principle 28
2.5 Existence and nonexistence of eigenvalues 36
2.6 Local definiteness 39
2.7 Definite eigenvalue problems 42
2.8 Sequences of compact Hermitian operators 45
2.9 Continuity of eigenvalues 47
2.10 Notes for Chapter 2 48
CWFTER 3 : Mul ti parameter eigenvalue problems for unbounded operators 50
3.1 Introduction 50
3.2 Semi bounded operators with compact resolvent 51
3.3 Transformation of eigenvalue problems 56
3.4 Definiteness conditions 60
3.5 Mul ti parameter boundary eigenvalue problems 61
3.6 Definiteness conditions for boundary eigenvalue problems 65
3.7 Klein s oscillation theorem 67
3.8 Stieltjes theorem on the zeros of Lame polynomials 70
3.9 Notes for Chapter 3 74
VI
CHAPTER 4 : Multiparameter expansion theorems for Hermitian matrices 76
4.1 Introduction 76
4.2 The tensor product of finite dimensional spaces 76
4.3 Completeness of eigenvectors 77
4.4 Positive definite form determinants 83
4.5 The expansion theorem for definite problems 84
4.6 Notes for Chapter 4 86
CHAPTER 5 : Multi parameter expansion theorems for bounded operators 87
5.1 Introduction 87
5.2 A result on form determinants 88
5.3 Eigenvectors and eigenspaces 88
5.4 Approximation of eigenvalue problems 90
5.5 Minkowski matrices 94
5.6 The expansion theorem for left definite problems 96
5.7 The r operator 101
5.8 The expansion theorem for right definite problems 1°2
5.9 Multi parameter eigenvalue problems for integral operators 107
5.10 Notes for Chapter 5 113
CHAPTER 6 : Mul tiparameter expansion theorems for unbounded operators U6
6.1 Introduction 116
6.2 Forms and operators on tensor products 117
6.3 Transformation of eigenvectors 120
6.4 Left definite eigenvalue problems 122
6.5 Right definite eigenvalue problems 126
6.6 Separation of variables l28
6.7 Left definite boundary eigenvalue problems 129
6.8 Right definite boundary eigenvalue problems l32
6.9 Separation in ellipsoidal coordinates 135
6.10 The expansion in series of Lame products 138
6.11 Notes for Chapter 6 140
Bibliography 142
Index 154
|
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| indexdate | 2024-07-09T15:27:15Z |
| institution | BVB |
| isbn | 3540504796 0387504796 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000799204 |
| oclc_num | 230967173 |
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| physical | VI, 157 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Volkmer, Hans Verfasser aut Multiparameter eigenvalue problems and expansion theorems Hans Volkmer Berlin [u.a.] Springer 1988 VI, 157 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1356 Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Mehrparametrige Spektraltheorie (DE-588)4205934-3 gnd rswk-swf Eigenwertproblem (DE-588)4013802-1 gnd rswk-swf Eigenvektor (DE-588)4151198-0 gnd rswk-swf Mehrparametriges Eigenwertproblem (DE-588)4289221-1 gnd rswk-swf Mehrparametrige Spektraltheorie (DE-588)4205934-3 s DE-604 Mehrparametriges Eigenwertproblem (DE-588)4289221-1 s Eigenvektor (DE-588)4151198-0 s Eigenwertproblem (DE-588)4013802-1 s Spektraltheorie (DE-588)4116561-5 s Lecture notes in mathematics 1356 (DE-604)BV000676446 1356 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000799204&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Volkmer, Hans Multiparameter eigenvalue problems and expansion theorems Lecture notes in mathematics Spektraltheorie (DE-588)4116561-5 gnd Mehrparametrige Spektraltheorie (DE-588)4205934-3 gnd Eigenwertproblem (DE-588)4013802-1 gnd Eigenvektor (DE-588)4151198-0 gnd Mehrparametriges Eigenwertproblem (DE-588)4289221-1 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4205934-3 (DE-588)4013802-1 (DE-588)4151198-0 (DE-588)4289221-1 |
| title | Multiparameter eigenvalue problems and expansion theorems |
| title_auth | Multiparameter eigenvalue problems and expansion theorems |
| title_exact_search | Multiparameter eigenvalue problems and expansion theorems |
| title_full | Multiparameter eigenvalue problems and expansion theorems Hans Volkmer |
| title_fullStr | Multiparameter eigenvalue problems and expansion theorems Hans Volkmer |
| title_full_unstemmed | Multiparameter eigenvalue problems and expansion theorems Hans Volkmer |
| title_short | Multiparameter eigenvalue problems and expansion theorems |
| title_sort | multiparameter eigenvalue problems and expansion theorems |
| topic | Spektraltheorie (DE-588)4116561-5 gnd Mehrparametrige Spektraltheorie (DE-588)4205934-3 gnd Eigenwertproblem (DE-588)4013802-1 gnd Eigenvektor (DE-588)4151198-0 gnd Mehrparametriges Eigenwertproblem (DE-588)4289221-1 gnd |
| topic_facet | Spektraltheorie Mehrparametrige Spektraltheorie Eigenwertproblem Eigenvektor Mehrparametriges Eigenwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000799204&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT volkmerhans multiparametereigenvalueproblemsandexpansiontheorems |