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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Sousa, Ruben¹  Guerra, Manuel^2,3  Yakubovich, Semyon¹ 

[1] Univ Porto, Fac Ciencias, Dept Matemat, CMUP, Rua Campo Alegre 687, P-4169007 Porto, Portugal

[2] Univ Lisbon, CEMAPRE, Rua Quelhas, P-1200781 Lisbon, Portugal

[3] Univ Lisbon, ISEG, Sch Econ & Management, Rua Quelhas, P-1200781 Lisbon, Portugal

关键词: Product formula;    Whittaker function;    Index Whittaker transform;    Generalized convolution;    Wiener-Levy theorem;    Convolution integral equations;   

DOI  :  10.1016/j.jmaa.2019.03.009

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free