Generalized Sonine-type integral transforms on the real line

Abstract

Starting from a generalized Sonine-type integral representation for the normalized Bessel functions (which was given earlier by Srivastava [H.M. Srivastava, A note on a generalization of Sonine's first finite integral, Matematiche (Catania) 23 (1968), pp. 1–6]), we construct a generalized Sonine (respectively, Sonine–Dunkl) integral transform on ℝ, which turns out (together with its dual) to be intertwining operators between Bessel (respectively, Dunkl) operators and certain singular differential (respectively, differential-difference) operators on ℝ.