Lanterna Rally

Author: S B Yakubovich

Publisher: World Scientific

Published: 1996-02-29

Total Pages: 264

ISBN-13: 9814500607

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. Contents:PreliminariesThe Kontorovich–Lebedev TransformThe Mehler–Fock TransformConvolution of the Kontorovich–Lebedev TransformGeneral Index TransformsIndex Transforms of the Lebedev–Skalskaya TypeIndex Tranforms with Hypergeometric Functions in the Kernel Readership: Researchers in mathematical analysis. keywords:Integral Transforms;Convolution;Fourier Transform;Mellin Transform;Kontorovich-Lebedev Transform;Index Transform;Hankel Transform;Mehler-Fock Transform;Olevskii Transform “It is a very well written book and the presentation of the material is commendable. In conclusion, it is useful book for research workers in the fields of integral transforms, special functions and fractional calculus.” Mathematics Abstracts “This is a well written book and it will be of interest not only to researchers but also to graduate students who are interested in the theory of integral transformations.” Mathematical Reviews “… This book presents a rather systematic and lucid account of the theory and applications of a fairly large variety of index transformations whose kernels involve not only the familiar Legendre and modified Bessel (or Macdonald) functions, but indeed also the Gaussian and other generalized hypergeometric functions, Meijer's G-function, and Foxs H-function. This state-of-the-art presentation of index transformations is recommended to all those graduate students and researchers (and other users of mathematics) who may find the various mathematical tools developed in this book to be potentially applicable in their works …” From the Foreword by H M Srivastava