In this article, we consider the Schrödinger semigroup related to the Dunkl–Laplacian Δ μ (associated to finite reflection group G) on R n . We characterize the image of L2(Rn,eu2hμ(u)du) under the Schrödinger semigroup as a reproducing kernel Hilbert space. We define Dunkl–Sobolev space in L2(Rn,eu2hμ(u)du) and characterize it’s image under the Schrödinger semigroup associated to G=Z2n as a reproducing kernel Hilbert space up to equivalence of norms. Also we provide similar results for Schrödinger semigroup associated to Dunkl–Hermite operator. © 2017, Springer International Publishing AG, part of Springer Nature.