On the product formula and convolution associated with the index Whittaker transform

Abstract

We deduce a product formula for the Whittaker $W$ function whose kernel does not depend on the second parameter. Making use of this formula, we define the positivity-preserving convolution operator associated with the index Whittaker transform, which is seen to be a direct generalization of the Kontorovich-Lebedev convolution. The mapping properties of this convolution operator are investigated; in particular, a Banach algebra property is established and then applied to yield an analogue of the Wiener-Lévy theorem for the index Whittaker transform. We show how our results can be used to prove the existence of a unique solution for a class of convolution-type integral equations.

24 pages. Accepted for publication in Journal of Mathematical Analysis and Applications

References in corpus (1)

• The spectral expansion approach to index transforms and connections with the theory of diffusion processes

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