On the images of Dunkl-Sobolev spaces under the Schroedinger semigroup associated to Dunkl operators

摘要

In this article, we consider the Schrodinger semigroup related to the Dunkl-Laplacian (associated to finite reflection group G) on Rn. We characterize the image of L2(Rn,eu2h(u)du) under the Schrodinger semigroup as a reproducing kernel Hilbert space. We define Dunkl-Sobolev space in L2(Rn,eu2h(u)du) and characterize it's image under the Schrodinger semigroup associated to G=Z2n as a reproducing kernel Hilbert space up to equivalence of norms. Also we provide similar results for Schrodinger semigroup associated to Dunkl-Hermite operator.