A Convolution Operator Related to the Generalized Mehler-Fock and Kontorovich-Lebedev Transforms

• Type: Article in International Scientific Journal
• Date: 2013

Authors

Rodrigues, MM (Author) FCUP; Vieira, N (Author) FCUP; Yakubovich, S (Author) FCUP

Journal

Title: Results in Mathematics

Vol. 63

Pages: 511-528

ISSN: 1422-6383

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 7 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-002-107

DOI: 10.1007/s00025-011-0214-x

Abstract (EN): In this paper we study a generalization of an index integral involving the product of modified Bessel functions and associated Legendre functions. It is applied to a convolution construction associated with this integral, which is related to the classical Kontorovich-Lebedev and generalized Mehler-Fock transforms. Mapping properties and norm estimates in weighted L (p) -spaces, 1 a parts per thousand currency sign p a parts per thousand currency sign 2, are investigated. An application to a class of convolution integral equations is considered. Necessary and sufficient conditions are found for the solvability of these equations in L (2).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 18