BESSEL TYPE INTEGRAL TRANSFORMATION AND I TS COMPOSITION WITH THE INTEGRAL AND DIFFERENTIAL OPERATOR

This article is concerned with the investigation of an integral transf ormation with the nucleus closely connected with the modified Bessel f unction of the third kind K(nu) (x). The conditions for the existence and for the boundedness in L(p)-spaces with degree weight are given an d its Mellin transformation is calculated. The composition formulae wi th Riemann-Liouville fractional integrodifferentiation operators on a half-axis and with the differential operator of the second order are p roved. As applications the compositions with Bessel operator and with the angular momentum operator widely used in potential theory and in q uantum mechanics are considered.