Positive definite and definitizable functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Akad.-Verl.
1994
|
| Edition: | 1. ed. |
| Series: | Mathematical topics
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 208 S. |
| ISBN: | 3055014464 |
Staff View
MARC
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| 100 | 1 | |a Sasvári, Zoltán |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Positive definite and definitizable functions |c Zoltán Sasvári |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1994 | |
| 300 | |a 208 S. | ||
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| 490 | 1 | |a Mathematical topics |v 2 | |
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Record in the Search Index
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| adam_text | Contents
1 Positive definite functions 9
1.1 Notation and preliminaries 9
1.2 Inner product spaces defined by complex valued functions .... 12
1.3 Construction of the Hilbert space H(f) 14
1.4 Some inequalities 21
1.5 Convergence of positive definite functions 25
1.6 Convolution and positive definite functions 27
1.7 Integrally positive definite functions 32
1.8 Extremal positive definite functions and irreducible representations 34
1.9 Bochner s theorem 43
1.10 Examples of positive definite functions 53
2 Some applications of positive definite functions 65
2.1 Duality of abelian groups 65
2.2 Spectral decomposition of unitary representations of abelian groups 69
2.3 Unitary representations of compact groups 73
3 Decomposition of positive definite functions 81
3.1 Decomposition of measurable positive definite functions 81
3.2 Decomposition of arbitrary positive definite functions 83
3.3 A finer decomposition 85
3.4 Equivalence of local and global measurability 90
4 Extension of positive definite functions 95
4.1 Extension from symmetric sets 95
4.2 The one dimensional case 100
4.3 The multidimensional case 105
4.4 Extension from subgroups 110
8 Contents
5 Functions with a finite number of negative squares 117
5.1 Definition and connection with unitary representations in
Pontryagin spaces 117
5.2 Characterization of bounded functions with k negative squares . 123
5.3 Measurable functions with k negative squares 125
5.4 Functions of finite rank 129
5.5 Definitizability of functions with k negative squares 134
6 Definitizable functions 137
6.1 Definition and some simple properties 137
6.2 The singularities of definitizable functions 141
6.3 Functions of finite order 146
6.4 Integral representation of functions / 6 Pc(j,k) with 7 (E F . . . 153
6.5 Further results 161
6.6 The singularities of a function with k negative squares 163
Appendix 169
A Pontryagin spaces 169
B Invariant subspaces of unitary operators in Pontryagin spaces . . 181
Bibliography 190
Index 203
List of symbols 207
|
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| id | DE-604.BV008377690 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:18:56Z |
| institution | BVB |
| isbn | 3055014464 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005524845 |
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| physical | 208 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical topics |
| series2 | Mathematical topics |
| spelling | Sasvári, Zoltán Verfasser aut Positive definite and definitizable functions Zoltán Sasvári 1. ed. Berlin Akad.-Verl. 1994 208 S. txt rdacontent n rdamedia nc rdacarrier Mathematical topics 2 Positive-definite functions Positiv-definite Funktion (DE-588)4175422-0 gnd rswk-swf Positiv-definite Funktion (DE-588)4175422-0 s DE-604 Mathematical topics 2 (DE-604)BV008671507 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005524845&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sasvári, Zoltán Positive definite and definitizable functions Mathematical topics Positive-definite functions Positiv-definite Funktion (DE-588)4175422-0 gnd |
| subject_GND | (DE-588)4175422-0 |
| title | Positive definite and definitizable functions |
| title_auth | Positive definite and definitizable functions |
| title_exact_search | Positive definite and definitizable functions |
| title_full | Positive definite and definitizable functions Zoltán Sasvári |
| title_fullStr | Positive definite and definitizable functions Zoltán Sasvári |
| title_full_unstemmed | Positive definite and definitizable functions Zoltán Sasvári |
| title_short | Positive definite and definitizable functions |
| title_sort | positive definite and definitizable functions |
| topic | Positive-definite functions Positiv-definite Funktion (DE-588)4175422-0 gnd |
| topic_facet | Positive-definite functions Positiv-definite Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005524845&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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