✦ LIBER ✦

A Class of Index Transforms with General Kernels

✍ Scribed by S. B. Yakubovich; Brian Fisher

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 652 KB
Volume: 200
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19992000108

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✦ Synopsis

Abstract

This paper deals with a class of integral transforms of the non ‐ convolution type involving sufficiently general kernels, which depend upon two essentially independent arguments. One of them, in various particular cases, is a parameter or index of the corresponding special functions. This class of integral transforms comprises the famous Kontorovich‐Lebedev and Mehler‐Fock transforms. We study here the mapping properties and give also inversion theorems of the general index transforms on the space L~p~(ℝ), p ≥ 1, that covers the respective measurable functions on the whole real axis with the norm
It is shown that the images of the transforms belong to the space L~ν, p~(ℝ~+~), νε ℝ, 1 ≤ p ≤ ∞ of functions normed by
In particular, when v = 1/p we get the usual L~p~(ℝ~+~) space. We also direct our attention to the case of the Hilbert space and give certain interesting examples of these transforms.

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