The hypergeometric approach to integral transforms and convolutions:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1994
|
| Schriftenreihe: | Mathematics and its applications
287 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006470559&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 324 S. |
| ISBN: | 0792328566 |
Internformat
MARC
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| 100 | 1 | |a Jakubovič, Semen B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The hypergeometric approach to integral transforms and convolutions |c by Semen B. Yakubovich and Yurii F. Luchko |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1994 | |
| 300 | |a XI, 324 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 287 | |
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Datensatz im Suchindex
| _version_ | 1819348811327209472 |
|---|---|
| adam_text | Contents
Preface ix
1 Preliminaries 1
1.1 Some special functions 1
1.2 Integral transforms 8
2 Mellin Convolution Type Transforms With Arbitrary Kernels 15
2.1 General Fourier kernels 15
2.2 Examples of the Fourier kernels 18
2.3 Watson type kernels 25
2.4 Bilateral Watson transforms 30
2.5 Multidimensional Watson transforms 34
3 H and G transforms 41
3.1 Mellin convolution type transform with Fox s H function as a kernel . 41
3.2 Mellin convolution type transforms with Meijer s G function as a kernel 50
3.3 The Erdelyi Kober fractional integration operators 54
4 The Generalized H and G transforms 59
4.1 The generalized H transform 59
4.2 The generalized G transform 62
4.3 Composition structure of generalized H and G transforms 64
5 The Generating Operators of Generalized H transforms 69
5.1 Generating operators in the space A4~* 69
5.2 Examples of the generating operators 75
6 The Kontorovich Lebedev Transform 79
6.1 The Kontorovich Lebedev transform: notion, existence and inversion
theorems in .M~*(£) spaces 79
6.2 The Kontorovich Lebedev transform in weighted L spaces 85
6.3 The Kontorovich Lebedev transform in weighted L2 spaces 94
6.4 The Kontorovich Lebedev transform of distributions 99
6.5 The Kontorovich Lebedev transform in XD spaces 103
v
7 General W transform and its Particular Cases 109
7.1 General G transform with respect to an index of the Kontorovich
Lebedev type 109
7.2 General W transform and its composition structure 118
7.3 Some particular cases of W transform and their properties 120
7.4 Fa transform 126
7.5 i2 theory of the Kontorovich Lebedev type index transforms 130
8 Composition Theorems of Plancherel Type for Index Transforms 139
8.1 Compositions with symmetric weight 139
8.2 Compositions with non symmetric weight 143
8.3 Constructions of index transforms in terms of Mellin integrals .... 145
9 Some Examples of Index Transforms and Their New Properties 149
9.1 The Kontorovich Lebedev like composition transforms 149
9.2 Some index transforms with symmetric kernels 153
9.3 The 3? and S index transforms 156
10 Applications to Evaluation of Index Integrals 167
10.1 Some useful representations and identities 168
10.2 Some general index integrals 171
11 Convolutions of Generalized H transforms 173
11.1 H convolutions 173
11.2 Examples of H convolutions 178
12 Generalization of the Notion of Convolution 183
12.1 Generalized H convolutions 183
12.2 Generalized G convolutions 187
13 Leibniz Rules and Their Integral Analogues 189
13.1 General Leibniz rules 190
13.2 Modified Leibniz rule 193
13.3 Leibniz rule for the Erdelyi Kober fractional differential operator . . . 195
13.4 Modification of the Leibniz rule for the Erdelyi Kober fractional dif¬
ferential operator 198
13.5 Integral analogues of Leibniz rules 202
14 Convolutions of Generating Operators 205
14.1 Convolutions in the Dimovski sense. General results 205
14.2 Examples of convolutions in the Dimovski sense 210
15 Convolution of the Kontorovich Lebedev Transform 213
15.1 Definition and some properties of a convolution for the Kontorovich
Lebedev transform 213
15.2 The basic property of convolution. Analogues with the Parseval equality218
vi
15.3 On the inversion of the Kontorovich Lebedev transform in the ring La 221
15.4 The space La as the commutative normed ring of functions with ex¬
ponential growth 223
16 Convolutions of the General Index Transforms 229
16.1 Convolutions of the Kontorovich Lebedev type transforms 229
16.2 The convolutions for the Mehler Fock and the Lebedev Skalskaya
transforms 236
16.3 The convolution of the Wimp Yakubovich type index transform . . . 238
17 Applications of the Kontorovich Lebedev type Convolutions to In¬
tegral Equations 241
17.1 Kontorovich Lebedev convolution equations of the second kind .... 241
17.2 General composition convolution equations 246
17.3 Some results on the homogeneous equation 247
18 Convolutional Ring Ca 253
18.1 Multiple Erdelyi Kober fractional integrodifferential operators .... 254
18.2 Convolutional ring Ca 261
19 The Fields of the Convolution Quotients 265
19.1 Extension of the ring (Ca,*,+) 265
19.2 Extension of the ring (La,*,+) 272
20 The Cauchy Problem for Erdelyi Kober Operators 277
20.1 General scheme 277
20.2 Differential equations of fractional order 279
20.3 Differential equations of hyper Bessel type 282
21 Operational Method of Solution of some Convolution Equations 287
21.1 Integral equations of Volterra type 287
21.2 Integral equations of second kind with Kontorovich Lebedev convolution292
References 295
Author Index 311
Subject Index 317
Notations 321
vii
|
| any_adam_object | 1 |
| author | Jakubovič, Semen B. Luchko, Yuri 1963- |
| author_GND | (DE-588)142680435 |
| author_facet | Jakubovič, Semen B. Luchko, Yuri 1963- |
| author_role | aut aut |
| author_sort | Jakubovič, Semen B. |
| author_variant | s b j sb sbj y l yl |
| building | Verbundindex |
| bvnumber | BV009778745 |
| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)844294272 (DE-599)BVBBV009778745 |
| dewey-full | 515.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.723 |
| dewey-search | 515.723 |
| dewey-sort | 3515.723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009778745 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:42:04Z |
| institution | BVB |
| isbn | 0792328566 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006470559 |
| oclc_num | 844294272 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-703 DE-11 |
| owner_facet | DE-12 DE-384 DE-703 DE-11 |
| physical | XI, 324 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spellingShingle | Jakubovič, Semen B. Luchko, Yuri 1963- The hypergeometric approach to integral transforms and convolutions Mathematics and its applications Hypergeometrische Reihe (DE-588)4161061-1 gnd Integraltransformation (DE-588)4027235-7 gnd |
| subject_GND | (DE-588)4161061-1 (DE-588)4027235-7 |
| title | The hypergeometric approach to integral transforms and convolutions |
| title_auth | The hypergeometric approach to integral transforms and convolutions |
| title_exact_search | The hypergeometric approach to integral transforms and convolutions |
| title_full | The hypergeometric approach to integral transforms and convolutions by Semen B. Yakubovich and Yurii F. Luchko |
| title_fullStr | The hypergeometric approach to integral transforms and convolutions by Semen B. Yakubovich and Yurii F. Luchko |
| title_full_unstemmed | The hypergeometric approach to integral transforms and convolutions by Semen B. Yakubovich and Yurii F. Luchko |
| title_short | The hypergeometric approach to integral transforms and convolutions |
| title_sort | the hypergeometric approach to integral transforms and convolutions |
| topic | Hypergeometrische Reihe (DE-588)4161061-1 gnd Integraltransformation (DE-588)4027235-7 gnd |
| topic_facet | Hypergeometrische Reihe Integraltransformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006470559&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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