Convolution operators on groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2011
|
| Schriftenreihe: | Lecture notes of the Unione Matematica Italiana
11 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XII, 171 S. 24 cm |
| ISBN: | 9783642206559 3642206557 |
Internformat
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Datensatz im Suchindex
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| adam_text |
IMAGE 1
CONTENTS
1 ELEMENTARY RESULTS 1
1. 1 BASIC NOTATIONS AND BASIC DEFINITIONS 1
1.1.1 RADON MEASURES AND INTEGRATION THEORY 1
1.1.2 LOCALLY COMPACT GROUPS 3
1.1.3 CONVOLUTION OF MEASURES AND FUNCTIONS 5
1.1.4 AMENABLE GROUPS 6
1.2 CONVOLUTION OPERATORS 7
1.3 FORG ABELIAN CV 2 (G) IS ISOMORPHIC TO L(G) 12
1.4 FORG ABELIAN CV P (G) IS ISOMORPHIC TO CV P (G) 16
1.5 CV P {G) AS A SUBSPACE OF CV 2 (G) 18
1.6 THE FOURIER TRANSFORM OF A CONVOLUTION OPERATOR 20
2 THE COMMUTATION'S THEOREM 25
2.1 THE CONVOLUTION OPERATOR TX P G {F) 25
2.2 A COMMUTATION PROPERTY OF CV 2 (G) 28
2.3 AN APPROXIMATION THEOREM FOR CV 2 (G) 31
3 THE FIGA-TALAMANCA HERZ ALGEBRA 33
3.1 DEFINITION OF A P (G) 33
3.2 A 2 (G) FORG ABELIAN 39
3.3 A P (G) IS A BANACH ALGEBRA 41
4 THEDUALOFZLP(G) 45
4.1 THE DUAL OF A P (G): THE NOTION OF PSEUDOMEASURE 45
4.2 APPLICATIONS TO ABELIAN GROUPS 52
4.3 HOLOMORPHIC FUNCTIONS OPERATING ON A P (G) 56
5 CV P (G) AS A MODULE ON A P (G) 65
5.1 THE CONVOLUTION OPERATOR (K * L)T 65
5.2 THE CONVOLUTION OPERATOR UT 68
IX
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010702955
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
5.3 CV P (G) AS A MODULE ON A P (G) 75
5.4 APPROXIMATION OF T BY (K * L)T FOR AN AMENABLE G 80
6 THE SUPPORT OF A CONVOLUTION OPERATOR 85
6.1 DEFINITION OF THE SUPPORT OF A CONVOLUTION OPERATOR 85
6.2 CHARACTERIZATION OF THE SUPPORT OF A PSEUDOMEASURE 88 6.3 A
GENERALIZATION OF WIENER'S THEOREM 91
6.4 AN APPROXIMATION THEOREM 94
6.5 APPLICATION TO AMENABLE GROUPS 96
7 CONVOLUTION OPERATORS SUPPORTED BY SUBGROUPS 101
7.1 THE IMAGE OF A CONVOLUTION OPERATOR 101
7.2 ON THE OPERATOR I(T) 107
7.3 A CANONICAL ISOMETRY OF CV P {H) INTO CV P {G) 112
7.4 THE SUPPORT OF/ (T) 118
7.5 THEOREMS OF DE LEEUW AND SAEKI 122
7.6 THE IMAGE OF THE MAP / 124
7.7 FIRST APPLICATIONS: THE THEOREM OF KAPLANSKY-HELSON 133 7.8 A
RESTRICTION PROPERTY FOR A P 136
7.9 SUBGROUPS AS SETS OF SYNTHESIS 141
8 C V P (G) AS A SUBSPACE OF CV 2 (G) 145
8.1 A CANONICAL MAP OF C(U(X, /*)) INTO C(L^(X,FI)) 145
8.2 AN INTEGRAL FORMULA FOR (TX P G (A)) L2(G) 150
8.3 C V 2 (G) AND C V P (G) IN AMENABLE GROUPS 156
NOTES 161
REFERENCES 167
LIST OF DEFINITIONS 171 |
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| author | Derighetti, Antoine |
| author_GND | (DE-588)124599109 |
| author_facet | Derighetti, Antoine |
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| author_sort | Derighetti, Antoine |
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| building | Verbundindex |
| bvnumber | BV039547196 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)725042775 (DE-599)DNB1010702955 |
| dewey-full | 515.785 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 512 - Algebra |
| dewey-raw | 515.785 512.55 |
| dewey-search | 515.785 512.55 |
| dewey-sort | 3515.785 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039547196 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-21T00:07:58Z |
| institution | BVB |
| isbn | 9783642206559 3642206557 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024399144 |
| oclc_num | 725042775 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM |
| owner_facet | DE-19 DE-BY-UBM |
| physical | XII, 171 S. 24 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes of the Unione Matematica Italiana |
| series2 | Lecture notes of the Unione Matematica Italiana |
| spelling | Derighetti, Antoine Verfasser (DE-588)124599109 aut Convolution operators on groups Antoine Derighetti Berlin ; Heidelberg Springer 2011 XII, 171 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes of the Unione Matematica Italiana 11 Literaturangaben Faltungsoperator (DE-588)4388315-1 gnd rswk-swf Lokal kompakte Gruppe (DE-588)4168094-7 gnd rswk-swf Banach-Algebra (DE-588)4193187-7 gnd rswk-swf Lokal kompakte Gruppe (DE-588)4168094-7 s Faltungsoperator (DE-588)4388315-1 s Banach-Algebra (DE-588)4193187-7 s DE-604 Erscheint auch als Online-Ausgabe Convolution Operators on Groups Lecture notes of the Unione Matematica Italiana 11 (DE-604)BV022297190 11 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3705642&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024399144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Derighetti, Antoine Convolution operators on groups Lecture notes of the Unione Matematica Italiana Faltungsoperator (DE-588)4388315-1 gnd Lokal kompakte Gruppe (DE-588)4168094-7 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| subject_GND | (DE-588)4388315-1 (DE-588)4168094-7 (DE-588)4193187-7 |
| title | Convolution operators on groups |
| title_auth | Convolution operators on groups |
| title_exact_search | Convolution operators on groups |
| title_full | Convolution operators on groups Antoine Derighetti |
| title_fullStr | Convolution operators on groups Antoine Derighetti |
| title_full_unstemmed | Convolution operators on groups Antoine Derighetti |
| title_short | Convolution operators on groups |
| title_sort | convolution operators on groups |
| topic | Faltungsoperator (DE-588)4388315-1 gnd Lokal kompakte Gruppe (DE-588)4168094-7 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| topic_facet | Faltungsoperator Lokal kompakte Gruppe Banach-Algebra |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3705642&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024399144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022297190 |
| work_keys_str_mv | AT derighettiantoine convolutionoperatorsongroups |