H-Transforms: Theory and Applications

by Kilbas; Anatoly A.

ISBN13: 9780415299169

ISBN10: 0415299160

Format: Hardcover

Pub. Date: 2004-03-17

Publisher(s): CRC Press

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Summary

H-Transforms: Theory and Applications presents a unified approach to the study of a wide class of integral transforms containing H- functions as kernels-or H-Transforms-and their applications. It provides a general introduction to the theory of integral transforms and details the existence, representation, expansion, and properties of H-transforms. Discussions also include applications of integral transforms with kernels involving the Meijer G-transform and special functions of hypergeometric and Bessel type. This book will not only appeal to postgraduates and researchers in pure and applied, but also to specialists in physics, mechanics, and engineering.

Author Biography

Megumi Saigo is a Professor in the Department of Mathematics at the University of Fukuoka, Japan.

Preface

Definition, Representations and Expansions of the H-Function

(30)

Definition of the H-Function

(2)

Existence and Representations

(2)

Explicit Power Series Expansions

(2)

Explicit Power-Logarithmic Series Expansions

(2)

Algebraic Asymptotic Expansions at Infinity

(3)

Exponential Asymptotic Expansions at Infinity in the Case Δ > 0, a* = 0

(5)

Exponential Asymptotic Expansions at Infinity in the Case n = 0

(2)

Algebraic Asymptotic Expansions at Zero

(2)

Exponential Asymptotic Expansions at Zero in the Case Δ < 0, a* = 0

(3)

Exponential Asymptotic Expansions at Zero in the Case m = 0

(1)

Bibliographical Remarks and Additional Information on Chapter 1

(6)

Properties of the H-Function

(40)

Elementary Properties

(2)

Differentiation Formulas

(3)

Recurrence Relations and Expansion Formulas

(5)

Multiplication and Transformation Formulas

(2)

Mellin and Laplace Transforms of the H-Function

(5)

Hankel Transforms of the H-Function

(3)

Fractional Integration and Differentiation of the H-Function

(5)

Integral Formulas Involving the H-Function

(6)

Special Cases of the H-Function

(5)

Bibliographical Remarks and Additional Information on Chapter 2

(4)

H-Transform on the Space Lν,2

(22)

The H-Transform and the Space Lν,τ

(1)

The Mellin Transform on Lν,τ

(2)

Some Auxiliary Operators

(3)

Integral Representations for the H-Function

(5)

Lν,2-Theory of the General Integral Transform

(4)

Lν,2-Theory of the H-Transform

(4)

Bibliographical Remarks and Additional Information on Chapter 3

(3)

H-Transform on the Space Lν,τ

(40)

Lν,τ-Theory of the H-Transform When a* = Δ = 0 and Re(μ) = 0

(4)

Lν,τ-Theory of the H-Transform When a* = Δ = 0 and Re(μ) < 0

(3)

Lν,τ-Theory of the H-Transform When a* = 0, Δ > 0

100

(4)

Lν,τ-Theory of the H-Transform When a* = 0, Δ < 0

104

(3)

Lν,τ-Theory of the H-Transform When a* > 0

107

(1)

Boundedness and Range of the H-Transform When a*1 > 0 and a*2 > 0

108

(4)

Boundedness and Range of the H-Transform When a* > 0 and a*1 = 0 or a*2 = 0

112

(3)

Boundedness and Range of the H-Transform When a* > 0 and a*1 < 0 or a*2 < 0

115

(3)

Inversion of the H-Transform When Δ = 0

118

(3)

Inversion of the H-Transform When Δ ≠ 0

121

(5)

Bibliographical Remarks and Additional Information on Chapter 4

126

(7)

Modified H-Transforms on the Space Lν,τ

133

(32)

Modified H-Transforms

133

(1)

H1-Transform on the Space Lν,τ

134

(6)

H2-Transform on the Space Lν,τ

140

(5)

Hσ,κ-Transform on the Space Lν,τ

145

(5)

H1σ,κ-Transform on the Space Lν,τ

150

(5)

H2σ,κ-Transform on the Space Lν,τ

155

(5)

Bibliographical Remarks and Additional Information on Chapter 5

160

(5)

G-Transform and Modified G-Transforms on the Space Lν,τ

165

(38)

G-Transform on the Space Lν,τ

165

(8)

Modified G-Transforms

173

(2)

G1-Transform on the Space Lν,τ

175

(4)

G2-Transform on the Space Lν,τ

179

(4)

Gσ,κ-Transform on the Space Lν,τ

183

(5)

G1σ,κ-Transform on the Space Lν,τ

188

(5)

G2σ,κ-Transform on the Space Lν,τ

193

(4)

Bibliographical Remarks and Additional Information on Chapter 6

197

(6)

Hypergeometric Type Integral Transforms on the Space Lν,τ

203

(60)

Laplace Type Transforms

203

(3)

Meijer and Varma Integral Transforms

206

(6)

Generalized Whittaker Transforms

212

(4)

Dγ-Transforms

216

(3)

1F2-Transforms

219

(4)

2F1-Transforms

223

(4)

2F1-Transforms

227

(6)

Modified 2F1-Transforms

233

(5)

The Generalized Stieltjes Transform

238

(2)

pFq-Transform

240

(6)

The Wright Transform

246

(5)

Bibliographical Remarks and Additional Information on Chapter 7

251

(12)

Bessel Type Integral Transforms on the Space Lν,τ

263

(94)

The Hankel Transform

263

(7)

Fourier Cosine and Sine Transforms

270

(2)

Even and Odd Hilbert Transforms

272

(4)

The Extended Hankel Transform

276

(4)

The Hankel Type Transform

280

(5)

Hankel-Schwartz and Hankel-Clifford Transforms

285

(4)

The Transform Yη

289

(10)

The Struve Transform

299

(8)

The Meijer kη-Transform

307

(6)

Bessel Type Transforms

313

(8)

The Modified Bessel Type Transform

321

(4)

The Generalized Hardy-Titchmarsh Transform

325

(12)

The Lommel-Maitland Transform

337

(5)

Bibliographical Remarks and Additional Information on Chapter 8

342

(15)

Bibliography

357

(20)

Subject Index

377

(4)

Author Index

381

(4)

Symbol Index

385

H-Transforms: Theory and Applications

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