Overview

This work deals with the theory and some applications of integral transforms that involve integration with respect to an index or parameter of a special function of the hypergeometric type as the kernel (index transforms). The basic index transforms are considered, such as the Kontorovich-Lebedev transform, the Mehler-Fock transform, the Olevskii Transform and the Lebedev-Skalskaya transforms. The Lp theory of index transforms is discussed, and new index transforms and convolution constructions are demonstrated. The essential multidimensional Kontorovich-Lebedev transform is investigated. General index transform formulae are obtained. The connection between the multidimensional index kernels and G and H functions of several variables is presented. The book is self-contained, and includes a list of symbols with definitions, author and subject indices, and an up-to-date bibliography. This work should be of interest to researchers and graduate students in the mathematical and physical sciences whose work involves integral transforms and special functions.

Full Product Details

Author:   Semyon B Yakubovich (Univ Do Porto, Portugal)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
ISBN:  

9789810222161

ISBN 10:   9810222165
Pages:   264
Publication Date:   01 February 1996
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Hypergeometric type special functions; Fourier, Laplace and Mellin transforms; Mellin convolution type integral transforms; Kontorovich-Lebedev transform; Mehler-Fock index transform; the Kontorovich-Lebedev transform of arbitrary index; asymptotic expansions of the index transforms; index-convolution Kontorovich-Lebedev transform; generalized Mehler-Fock transform; the Olevskii index transform; the index transforms with hypergeometric functions as the kernels; index transforms with the product of legendre functions of the first and second kind; the Lebedev-Skalskaya index transforms; index transforms involving Meijer G and H functions as the kernels; index transforms with the Whittaker functions; index transforms with cylindrical functions; convolutions of the index transforms; index transforms of distributions; multidimensional Kontorovich-Lebedev transform; multidimensional index transforms.

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