On the generalized convolution for I-transform
The authors introduce the so-called \(I\)-transform, which generalizes integral transformations with the Meijer \(G\)-functions and the Fox \(H\)-functions as kernels. It can be written also in terms of the Mellin-Barnes integral. A generalized convolution is constructed for this transformation basing on the hypergeometric approach [see, for instance, in the monograph of \textit{S. B. Yakubovich} and \textit{Y. F. Luchko}, The hypergeometric approach to integral transforms and convolutions (Mathematics and its Applications 287, Kluwer, Dordrecht) (1994; Zbl 0803.44001)]. General theorems of the existence and mapping properties for this convolution are exhibited. Various examples of the method are given. It includes convolutions with the Bessel functions and the parabolic cylinder functions.
scientific article; zbMATH DE number 2076047