The generalization of shift operator related Bessel differential operator

Abstract

We introduce the generalized shift operator related to the Bessel differential operator and the Hankel integral transform. It generalizes the operator introduced by J Delsarte and studied by J. Delsarte, B.M. Levitan and Ya.I. Zhitomirskii. The considered operator is not the generalized shift operator of the Levitan’s type. The basic properties of the shift operator are proved. The visualization of shift action is given.