Index Transforms Associated with Bessel and Lommel Functions

Abstract

In this paper we extend a variety of index integral transforms (i.e. integral transforms over an index as integration variable) with Bessel and Lommel functions as kernels by considering mapping properties of the related integral operators. This class of transforms includes, for instance, operators of Titchmarsh type. Useful integral representations of the considered kernels are deduced and boundedness properties, Parseval equalities, Plancherel type theorem and inversion formula are given.