Index Transforms

Semyon B Yakubovich

• Publisher: World Scientific
• Year: 1996
• ISBN:
  9789812831064
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

This book 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 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. For the first time, the essentially multidimensional Kontorovich-Lebedev transform is announced. 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 will be of interest to researchers and graudate students in the mathematical and physical sciences whose work involves integral transforms and special functions.

Table of contents

• Contents
• Foreword
• Preface
• Chapter 1 Preliminaries
• Chapter 2 The Kontorovich-Lebedev Transform
• Chapter 3 The Mehler-Fock Transform
• Chapter 4 Convolution of the Kontorovich-Lebedev Transform
• Chapter 5 General Index Transforms
• Chapter 6 Index Transforms of The Lebedev-Skalskaya Type
• Chapter 7 Index Transforms with Hypergeometric Functions in The Kernel
• Bibliography
• Author Index
• Subject index
• Notations