Functional equations on hypergroups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2013
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 191 S. |
| ISBN: | 9789814407007 |
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MARC
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Record in the Search Index
| _version_ | 1804149678211596288 |
|---|---|
| adam_text | Titel: Functional Equations on Hypergroups
Autor: Székelyhidi, László
Jahr: 2013
Contents
Preface vii
1. Introduction 1
1.1 Basic concepts and facts................... 1
1.2 Convolution of subsets.................... 6
1.3 Invariant means on hyper groups .............. 7
1.4 Haar measure on hypergroups................ 11
1.5 Exponential functions on hypergroups........... 20
1.6 Exponential families on hypergroups............ 22
1.7 Additive and multi-additive functions on hypergroups . . 23
1.8 Moment functions on hypergroups............. 26
1.9 Exponentials and additive functions on a special
hypergroup.......................... 33
2. Polynomial hypergroups in one variable 37
2.1 Polynomial hypergroups in one variable.......... 37
2.2 Exponential and additive functions on polynomial
hypergroups.......................... 39
2.3 Moment functions on polynomial hypergroups....... 43
2.4 Moment functions on the S t/(2)-hypergroup........ 48
3. Polynomial hypergroups in several variables 51
3.1 Polynomial hypergroups in several variables........ 51
3.2 Exponential and additive functions on multivariate
polynomial hypergroups................... 52
3.3 Moment function sequences on multivariate polynomial
hypergroups.......................... 55
4. Sturm-Liouville hypergroups 59
4.1 Sturm-Liouville functions.................. 59
4.2 Exponentials and additive functions on Sturm-Liouville
hypergroups.......................... 62
4.3 Moment functions on Sturm-Liouville hypergroups .... 65
5. Two-point support hypergroups 73
5.1 Conditional functional equations.............. 73
5.2 Two-point support hypergroups of noncompact type ... 77
5.3 Moment functions on two-point support hypergroups of
noncompact type....................... 78
5.4 Two-point support hypergroups of compact type..... 86
5.5 The cosh hypergroup..................... 87
5.6 Associated pairs of moment functions ........... 88
6. Spectral analysis and synthesis on polynomial hypergroups 95
6.1 Spectral analysis and spectral synthesis on hypergroups . 95
6.2 Basic concepts and facts................... 96
6.3 Spectral analysis on polynomial hypergroups in a single
variable............................ 99
6.4 Exponential polynomials on polynomial hypergroups in a
single variable......................... 100
6.5 Spectral synthesis on polynomial hypergroups in a
single variable......................... 103
6.6 Spectral analysis and spectral synthesis on multivariate
polynomial hypergroups................... 103
6.7 Spectral analysis and moment functions.......... 106
7. Spectral analysis and synthesis on Sturm-Liouville hypergroups 109
7.1 Exponential monomials on Sturm-Liouville hypergroups . 109
7.2 Linear independence of special exponential monomials . . 110
7.3 Spectral analysis on Sturm-Liouville hypergroups..... 119
8. Moment problems on hypergroups 123
8.1 The moment problem in general .............. 123
8.2 Uniqueness on polynomial hypergroups........... 124
8.3 The case of Sturm-Liouville hypergroups ......... 128
8.4 An approximation result................... 131
9. Special functional equations on hypergroups 133
9.1 The sine functional equation on polynomial
hypergroups.......................... 133
9.2 The cosine functional equation on polynomial
hypergroups.......................... 138
9.3 The Levi-Civita functional equation............ 142
10. Difference equations on polynomial hypergroups 149
10.1 Introduction.......................... 149
10.2 Difference equations with 1-translation........... 150
10.3 Difference equations with general translation....... 153
11. Stability problems on hypergroups 161
11.1 Stability of exponential functions on hypergroups..... 161
11.2 Stability of additive functions on hypergroups....... 163
11.3 Superstability of a mixed-type functional equation .... 165
11.4 Superstability of generalized moment functions on
hypergroups.......................... 168
Bibliography 173
Index 187
|
| any_adam_object | 1 |
| author | Székelyhidi, László 1977- |
| author_GND | (DE-588)129186236 |
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| author_sort | Székelyhidi, László 1977- |
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| building | Verbundindex |
| bvnumber | BV040592123 |
| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)820425620 (DE-599)HBZHT017259767 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040592123 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:26:51Z |
| institution | BVB |
| isbn | 9789814407007 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025420031 |
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| owner_facet | DE-824 DE-19 DE-BY-UBM |
| physical | XVII, 191 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Székelyhidi, László 1977- Verfasser (DE-588)129186236 aut Functional equations on hypergroups Laszlo Szekelyhidi Singapore [u.a.] World Scientific 2013 XVII, 191 S. txt rdacontent n rdamedia nc rdacarrier Hypergruppe (DE-588)4561851-3 gnd rswk-swf Funktionalgleichung (DE-588)4018923-5 gnd rswk-swf Hypergruppe (DE-588)4561851-3 s Funktionalgleichung (DE-588)4018923-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025420031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Székelyhidi, László 1977- Functional equations on hypergroups Hypergruppe (DE-588)4561851-3 gnd Funktionalgleichung (DE-588)4018923-5 gnd |
| subject_GND | (DE-588)4561851-3 (DE-588)4018923-5 |
| title | Functional equations on hypergroups |
| title_auth | Functional equations on hypergroups |
| title_exact_search | Functional equations on hypergroups |
| title_full | Functional equations on hypergroups Laszlo Szekelyhidi |
| title_fullStr | Functional equations on hypergroups Laszlo Szekelyhidi |
| title_full_unstemmed | Functional equations on hypergroups Laszlo Szekelyhidi |
| title_short | Functional equations on hypergroups |
| title_sort | functional equations on hypergroups |
| topic | Hypergruppe (DE-588)4561851-3 gnd Funktionalgleichung (DE-588)4018923-5 gnd |
| topic_facet | Hypergruppe Funktionalgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025420031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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