Index transforms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 248 S. |
| ISBN: | 9810222165 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Foreword v
Preface xi
1 Preliminaries 1
1.1 The spaces Lp and Lp(p) 1
1.2 Special functions of the hypergeometric type 5
1.3 Fourier s, Mellin s and Laplace s transforms 30
1.4 General Mellin convolution type integral transforms 34
1.5 Notion of the index transforms 36
2 The Kontorovich Lebedev Transform 39
2.1 Definition, inversion in L^p 39
2.2 Note on the K L summability of integrals 46
2.3 The space Ii,2(R+). Parseval s relation. Plancherel s theorem .... 48
2.4 Composition representations of the K L transform.
A convolution Hilbert space 54
2.5 Representations through the Mellin transform. Watson s
type lemma 62
2.6 The index convolution Kontorovich Lebedev transform 68
3 The Mehler Fock Transform 75
3.1 Definition. Inversion in Lp space 75
3.2 The composition theorem of inversion 90
3.3 The generalized Mehler Fock transform 92
3.4 Parseval s equality 95
3.5 An index convolution transform related to the Mehler Fock
integral 101
4 Convolution of the Kontorovich Lebedev Transform 105
4.1 Definition of the convolution. Useful estimates 105
4.2 The factorization property. Parseval s type equality 112
4.3 The space La as a normed ring 117
4.4 Convolution Hilbert spaces 122
4.5 On the Kontorovich Lebedev convolution integral equations 131
4.6 Other convolution constructions 136
ix
x Index Transforms
5 General Index Transforms 143
5.1 The Kontorovich Lebedev transform in a complex domain.
Analogs of the Hardy type spaces and the Paley Wiener theorem . . . 144
5.2 Composition theorems for general index transforms 156
5.3 Watson s type kernels 162
5.4 Compositions with the Mellin Barnes integrals 168
6 Index Transforms of The Lebedev Skalskaya Type 171
6.1 Useful representations and estimates 172
6.2 The Lebedev Skalskaya transforms 175
6.3 /^ theory of the Lebedev Skalskaya transforms 183
6.4 Convolution representations 190
7 Index Transforms with Hypergeometric Functions in
The Kernel 199
7.1 Index transforms of the Olevskii type 200
7.2 General ^ transforms 209
7.3 Note on the essentially multidimensional Kontorovich Lebedev
transform 221
Bibliography 225
Author Index 239
Subject Index 243
Notations 247
|
| any_adam_object | 1 |
| author | Yakubovich, Semen B. |
| author_facet | Yakubovich, Semen B. |
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| author_sort | Yakubovich, Semen B. |
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| dewey-full | 515.43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.43 |
| dewey-search | 515.43 |
| dewey-sort | 3515.43 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012741599 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:32:53Z |
| institution | BVB |
| isbn | 9810222165 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008664341 |
| oclc_num | 35044928 |
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| owner | DE-703 DE-188 |
| owner_facet | DE-703 DE-188 |
| physical | XIII, 248 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Yakubovich, Semen B. Verfasser aut Index transforms S. B. Yakubovich Singapore [u.a.] World Scientific 1996 XIII, 248 S. txt rdacontent n rdamedia nc rdacarrier Integral transforms Transformations (Mathematics) Integraltransformation (DE-588)4027235-7 gnd rswk-swf Integraltransformation (DE-588)4027235-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008664341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yakubovich, Semen B. Index transforms Integral transforms Transformations (Mathematics) Integraltransformation (DE-588)4027235-7 gnd |
| subject_GND | (DE-588)4027235-7 |
| title | Index transforms |
| title_auth | Index transforms |
| title_exact_search | Index transforms |
| title_full | Index transforms S. B. Yakubovich |
| title_fullStr | Index transforms S. B. Yakubovich |
| title_full_unstemmed | Index transforms S. B. Yakubovich |
| title_short | Index transforms |
| title_sort | index transforms |
| topic | Integral transforms Transformations (Mathematics) Integraltransformation (DE-588)4027235-7 gnd |
| topic_facet | Integral transforms Transformations (Mathematics) Integraltransformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008664341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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