Index Transforms

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.