Index transforms
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書誌事項
Index transforms
World Scientific, c1996
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内容説明・目次
内容説明
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.
目次
- 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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