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

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Sousa, R (Author) Other; Guerra, M (Author) Other; Yakubovich, SB (Author) FCUP

Journal

Title: Journal of Mathematical Analysis and Applications

Vol. 475

Pages: 939-965

ISSN: 0022-247X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 0 Citations

Other information

Authenticus ID: P-00Q-G0K

DOI: 10.1016/j.jmaa.2019.03.009

Abstract (EN): We deduce a product formula for the Whittaker function W-kappa,W-mu 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-Levy 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 27