H-transforms theory and applications
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| Format: | Buch |
| Sprache: | English |
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Boca Raton, FL [u.a.]
Chapman & Hall/CRC
2004
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| Schriftenreihe: | Analytical methods and special functions
9 |
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| 100 | 1 | |a Kilbas, Anatolij A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a H-transforms |b theory and applications |c Anatoly A. Kilbas ; Megumi Saigo |
| 264 | 1 | |a Boca Raton, FL [u.a.] |b Chapman & Hall/CRC |c 2004 | |
| 300 | |a XII, 389 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Analytical methods and special functions |v 9 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Fonctions H | |
| 650 | 4 | |a Transformations intégrales | |
| 650 | 4 | |a H-functions | |
| 650 | 4 | |a Integral transforms | |
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| 700 | 1 | |a Saigo, Megumi |e Verfasser |4 aut | |
| 830 | 0 | |a Analytical methods and special functions |v 9 |w (DE-604)BV011932737 |9 9 | |
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Datensatz im Suchindex
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| adam_text | H-TRANSFORMS THEORY AND APPLICATIONS ANATOLYA. KILBAS BELARUSIAN STATE
UNIVERSITY, BELARUS MEGUMI SAIGO FUKUOKA UNIVERSITY, JAPAN CHAPMAN &
HALL/CRC A CRC PRESS COMPANY BOCA RATON LONDON NEW YORK WASHINGTON, D.C.
CONTENTS PREFACE IX CHAPTER 1. DEFINITION, REPRESENTATIONS AND
EXPANSIONS OF THE H -FUNCTION 1 1.1. DEFINITION OF THE .FF-FUNCTION 1
1.2. EXISTENCE AND REPRESENTATIONS 3 1.3. EXPLICIT POWER SERIES
EXPANSIONS 5 1.4. EXPLICIT POWER-LOGARITHMIC SERIES EXPANSIONS 7 1.5.
ALGEBRAIC ASYMPTOTIC EXPANSIONS AT INFINITY 9 1.6. EXPONENTIAL
ASYMPTOTIC EXPANSIONS AT INFINITY IN THE CASE A 0, O* = 0 12 1.7.
EXPONENTIAL ASYMPTOTIC EXPANSIONS AT INFINITY IN THE CASE N = 0 17 1.8.
ALGEBRAIC ASYMPTOTIC EXPANSIONS AT ZERO 19 1.9. EXPONENTIAL ASYMPTOTIC
EXPANSIONS AT ZERO IN THE CASE A 0, O* = 0 21 1.10. EXPONENTIAL
ASYMPTOTIC EXPANSIONS AT ZERO IN THE CASE M = 0 24 1.11. BIBLIOGRAPHICAL
REMARKS AND ADDITIONAL INFORMATION ON CHAPTER 1 25 CHAPTER 2. PROPERTIES
OF THE FF-FUNCTION 3 1 2.1. ELEMENTARY PROPERTIES , 31 2.2.
DIFFERENTIATION FORMULAS 33 2.3. RECURRENCE RELATIONS AND EXPANSION
FORMULAS 36 2.4. MULTIPLICATION AND TRANSFORMATION FORMULAS 41 2.5.
MELLIN AND LAPLACE TRANSFORMS OF THE IF-FUNCTION 43 2.6. HANKEL
TRANSFORMS OF THE I?-FUNCTION 48 2.7. FRACTIONAL INTEGRATION AND
DIFFERENTIATION OF THE IL-FUNCTION 51 2.8. INTEGRAL FORMULAS INVOLVING
THE FF-FUNCTION 56 2.9. SPECIAL CASES OF THE H-FUNCTION 62 2.10.
BIBLIOGRAPHICAL REMARKS AND ADDITIONAL INFORMATION ON CHAPTER 2 67 VI
CONTENTS CHAPTER 3. H-TRANSFORM ON THE SPACE ^2 71 3.1. THE
IF-TRANSFORM AND THE SPACE Z VYT 71 3.2. THE MELLIN TRANSFORM ON *,,.
72 3.3. SOME AUXILIARY OPERATORS 74 3.4. INTEGRAL REPRESENTATIONS FOR
THE IJ-FUNCTION 77 3.5. ^2-THEORY OF THE GENERAL INTEGRAL TRANSFORM 82
3.6. ^,2-THEORY OF THE IF-TRANSFORM 86 3.7. BIBLIOGRAPHICAL REMARKS AND
ADDITIONAL INFORMATION ON CHAPTER 3 90 CHAPTER 4. IF-TRANSFORM ON THE
SPACE *,,. 93 4.1. ^-THEORY OF THE IF-TRANSFORM WHEN A* = A = 0 AND
RE(/X) = 0 93 4.2. FI^-THEORY OF THE IF-TRANSFORM WHEN A* = A = 0 AND
RE(/Z) 0 97 4.3. ^-THEORY OF THE IF-TRANSFORM WHEN A* = 0, A 0 100
4.4. ,, IR -THEORY OF THE IF-TRANSFORM WHEN A* = 0, A 0 104 4.5.
FI^-THEORY OF THE IF-TRANSFORM WHEN A* 0 107 4.6. BOUNDEDNESS AND
RANGE OF THE IF-TRANSFORM WHEN A 0 AND A 0 108 4.7. BOUNDEDNESS
AND RANGE OF THE H -TRANSFORM WHEN A* 0 AND AJ = 0 OR A* 2 = 0 112
4.8. BOUNDEDNESS AND RANGE OF THE FF-TRANSFORM WHEN A* 0 AND A 0 OR
02 0 115 4.9. INVERSION OF THE H-TRANSFORM WHEN A = 0 118 4.10.
INVERSION OF THE H-TRANSFORM WHEN A^0 121 4.11. BIBLIOGRAPHICAL REMARKS
AND ADDITIONAL INFORMATION ON CHAPTER 4 126 CHAPTER 5. MODIFIED
FF-TRANSFORMS ON THE SPACE *,,. 133 5.1. MODIFIED H-TRANSFORMS 133 5.2.
H ^TRANSFORM ON THE SPACE *,,. 134 5.3. H 2 -TRANSFORM ON THE SPACE
*,,. 140 5.4. IF^K-TRANSFORM ON THE SPACE *,,. 145 5.5. H ^-TRANSFORM
ON THE SPACE L U ^ R 150 5.6. H ^-TRANSFORM ON THE SPACE ^ R 155 5.7.
BIBLIOGRAPHICAL REMARKS AND ADDITIONAL INFORMATION ON CHAPTER 5 160
CONTENTS CHAPTER 6. G- TRANSFORM AND MODIFIED G-TRANSFORMS ON THE SPACE
U R 165 6.1. G- TRANSFORM ON THE SPACE Z V}T 165 6.2. MODIFIED G-
TRANSFORMS 173 6.3. G^TRANSFORM ON THE SPACE , V R 175 6.4. G 2
-TRANSFORM ON THE SPACE V 179 6.5. G^-TRANSFORM ON THE SPACE *,,. 183
6.6. G* B -TRANSFORM ON THE SPACE *,,. 188 6.7. G K -TRANSFORM ON THE
SPACE *,,. 193 6.8. BIBLIOGRAPHICAL REMARKS AND ADDITIONAL INFORMATION
ON CHAPTER 6 197 CHAPTER 7. HYPERGEOMETRIC TYPE INTEGRAL TRANSFORMS ON
THE SPACE *,,. 203 7.1. LAPLACE TYPE TRANSFORMS 203 7.2. MEIJER AND
VARMA INTEGRAL TRANSFORMS 7.3. GENERALIZED WHITTAKER TRANSFORMS 7.4. .D
7 -TRANSFORMS 7.5. X.FI-TRANSFBRMS 7.6. I I^-TRANSFORMS 7.7.
2-^I-TRANSFORMS 7.8. MODIFIED 2 -FI-TRANSFORMS 7.9. THE GENERALIZED
STIELTJES TRANSFORM 7.10. PFG-TRANSFORM 7.11. TH E WRIGHT TRANSFORM 246
7.12. BIBLIOGRAPHICAL REMARKS AND ADDITIONAL INFORMATION ON CHAPTER 7
206 212 216 219 223 227 233 238 240 251 CHAPTER 8. BESSEL TYPE INTEGRAL
TRANSFORMS ON THE SPACE *,,. 263 8.1. THE HANKEL TRANSFORM 263 8.2.
FOURIER COSINE AND SINE TRANSFORMS 270 8.3. EVEN AND ODD HILBERT
TRANSFORMS 272 8.4. THE EXTENDED HANKEL TRANSFORM 276 8.5. THE HANKEL
TYPE TRANSFORM 280 8.6. HANKEL*SCHWARTZ AND HANKEL*CLIFFORD TRANSFORMS
285 VIII CONTENTS 8.7. THE TRANSFORM * 289 8.8. THE STRUVE TRANSFORM
299 8.9. THE MEIJER .^-TRANSFORM 307 8.10. BESSEL TYPE TRANSFORMS 313
8.11. THE MODIFIED BESSEL TYPE TRANSFORM 321 8.12. THE GENERALIZED
HARDY-TITCHMARSH TRANSFORM 325 8.13. THE LOMMEL-MAITLAND TRANSFORM 337
8.14. BIBLIOGRAPHICAL REMARKS AND ADDITIONAL INFORMATION ON CHAPTER 8
342 BIBLIOGRAPHY 357 SUBJECT INDEX 377 AUTHOR INDEX 381 SYMBOL INDEX 385
|
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| discipline | Mathematik |
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| id | DE-604.BV017747793 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T16:26:49Z |
| institution | BVB |
| isbn | 0415299160 |
| language | English |
| lccn | 2003070007 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010664382 |
| oclc_num | 53901321 |
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| physical | XII, 389 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Analytical methods and special functions |
| series2 | Analytical methods and special functions |
| spellingShingle | Kilbas, Anatolij A. Saigo, Megumi H-transforms theory and applications Analytical methods and special functions Fonctions H Transformations intégrales H-functions Integral transforms Integraltransformation (DE-588)4027235-7 gnd Thetafunktion (DE-588)4185175-4 gnd |
| subject_GND | (DE-588)4027235-7 (DE-588)4185175-4 |
| title | H-transforms theory and applications |
| title_auth | H-transforms theory and applications |
| title_exact_search | H-transforms theory and applications |
| title_full | H-transforms theory and applications Anatoly A. Kilbas ; Megumi Saigo |
| title_fullStr | H-transforms theory and applications Anatoly A. Kilbas ; Megumi Saigo |
| title_full_unstemmed | H-transforms theory and applications Anatoly A. Kilbas ; Megumi Saigo |
| title_short | H-transforms |
| title_sort | h transforms theory and applications |
| title_sub | theory and applications |
| topic | Fonctions H Transformations intégrales H-functions Integral transforms Integraltransformation (DE-588)4027235-7 gnd Thetafunktion (DE-588)4185175-4 gnd |
| topic_facet | Fonctions H Transformations intégrales H-functions Integral transforms Integraltransformation Thetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010664382&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932737 |
| work_keys_str_mv | AT kilbasanatolija htransformstheoryandapplications AT saigomegumi htransformstheoryandapplications |