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H-transforms: theory and applications

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Bibliographic Details
Main Authors:	Kilbas, Anatolij A. (Author), Saigo, Megumi (Author)
Format:	Book
Language:	English
Published:	Boca Raton, FL [u.a.] Chapman & Hall/CRC 2004
Series:	Analytical methods and special functions 9
Subjects:	Fonctions H Transformations intégrales H-functions Integral transforms Integraltransformation Thetafunktion
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	XII, 389 S.
ISBN:	0415299160

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MARC


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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. HANKELSCHWARTZ AND HANKELCLIFFORD 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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author	Kilbas, Anatolij A. Saigo, Megumi
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isbn	0415299160
language	English
lccn	2003070007
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series	Analytical methods and special functions
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spelling	Kilbas, Anatolij A. Verfasser aut H-transforms theory and applications Anatoly A. Kilbas ; Megumi Saigo Boca Raton, FL [u.a.] Chapman & Hall/CRC 2004 XII, 389 S. txt rdacontent n rdamedia nc rdacarrier Analytical methods and special functions 9 Includes bibliographical references and index Fonctions H Transformations intégrales H-functions Integral transforms Integraltransformation (DE-588)4027235-7 gnd rswk-swf Thetafunktion (DE-588)4185175-4 gnd rswk-swf Thetafunktion (DE-588)4185175-4 s Integraltransformation (DE-588)4027235-7 s b DE-604 Saigo, Megumi Verfasser aut Analytical methods and special functions 9 (DE-604)BV011932737 9 GBV Datenaustausch application/pdf 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 Inhaltsverzeichnis
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

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