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arXiv · 1802.06657

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

Rúben Sousa·Manuel Guerra·Semyon Yakubovich
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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.

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Rúben Sousa, Manuel Guerra, Semyon Yakubovich. 2019-03-21. On the product formula and convolution associated with the index Whittaker transform. https://doi.org/10.1016/j.jmaa.2019.03.009

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