On the problem of constructing integral transforms by means of composition technique
Along with classical transforms, such as Fourier, Mellin, Hankel, and those of convolution type, the modern investigations use integral transforms with respect to subscripts, such as Kantorovich-Lebedev's transform, Mehler-Fock's, Lebedev-Skal'skaya's, and other ones. By means of representation of integral transforms as compositions of known transforms and due to properties of the latter ones, in the present article we prove for the first time the composition theorems of Plancherel type for subscript transforms. We extend the composition method on Watson's general transforms and construct new integral transforms with respect to subscript of the Lommel function and of some parameters of Meijer's \(G\)-function.
scientific article; zbMATH DE number 819999