Sobolev spaces associated with a Dunkl type differential-difference operator on the real line and applications

Abstract

In this paper we study the Sobolev spaces associated with a Dunkl type differential-difference operator on the real line. As applications we study the theory of reproducing kernels to the Tikhonov regularization, on the generalized Sobolev spaces. We give some properties including some estimates for the solution of the generalized Schrodinger equation.