Dunkl-Schrödinger operators

Abstract

In this paper, we consider the Schrödinger operators $L_k=-{\Delta }_k+V$, where ${\Delta }_k$ is the Dunkl-Laplace operator and $V$ is a non-negative potential on $R^d$. We establish that $L_k$ is essentially self-adjoint on $C_0^{\infty }$. In particular, we develop a bounded $H^{\infty }$-calculus on $L^p$ spaces for the Dunkl harmonic oscillator operator.