Amel Hammi | Searcharxiv

arXiv2019

Semigroup and Riesz transform for the Dunkl- Schrödinger operators

Let $L_k=-Δ_k+V$ be the Dunk- Schrödinger operators, where $Δ_k=\sum_{j=1}^dT_j^2$ is the Dunkl Laplace operator associated to the dunkl operators $T_j$ on $\mathbb{R}^d$ and $V$ is a nonnegative potential function. In the first part of this paper we introduce the Riesz transform $R_j= T_j L_k^{-1/2}$ as an $L^2$- bounded operator and we prove that is of weak type $(1,1)$ and then is bounded on $L^p(\mathbb{R}^d,dμ_k(x))$ for $1<p\leq 2$. The second pat is devoted to the $L^p$ smoothing of the semigroup generated by $L_k$, when $V$ belongs to the standard Koto class.

math.FA↗

arXiv2018

Dunkl-Schrödinger operators

In this paper, we consider the Schrödinger operators $L_k=-Δ_k+V$, where $Δ_k$ 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.

math.FA↗