This article is cited in 1 paper

Dunkl-Type Operators with Projections Terms Associated to Orthogonal Subsystems in Roots System

Fethi Bouzeffour

Department of Mathematics, King Saudi University, College of Sciences, P.O. Box 2455 Riyadh 11451, Saudi Arabia

Abstract: In this paper, we introduce a new differential-difference operator $T_\xi$ $(\xi \in \mathbb{R}^N)$ by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between $T_\xi$ and the directional derivative $\partial_\xi$. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this operator.

Keywords: special functions; differential-difference operators; integral transforms.

MSC: 33C15; 33D52; 35A22

Received: April 24, 2013; in final form October 16, 2013; Published online October 23, 2013

Language: English

DOI: 10.3842/SIGMA.2013.064

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ArXiv: 1304.5866