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INDEX TRANSFORMS
by S B Yakubovich (Belarusian State University, Minsk)
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:
- Preliminaries
- The Kontorovich–Lebedev Transform
- The
Mehler–Fock Transform
- Convolution of the Kontorovich–Lebedev Transform
- General Index Transforms
- Index Transforms of the Lebedev–Skalskaya Type
- Index Tranforms with Hypergeometric Functions in the Kernel
Readership: Researchers in mathematical analysis.
"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."
"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."
| 264pp |
Pub. date: Feb 1996 |
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