paper

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

arXiv:1802.06657 · doi:10.1016/j.jmaa.2019.03.009

Abstract

We deduce a product formula for the Whittaker 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

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