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This article is cited in 1 scientific paper (total 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.
Received: April 24, 2013; in final form October 16, 2013; Published online October 23, 2013
Citation:
Fethi Bouzeffour, “Dunkl-Type Operators with Projections Terms Associated to Orthogonal Subsystems in Roots System”, SIGMA, 9 (2013), 064, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma847 https://www.mathnet.ru/eng/sigma/v9/p64
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Abstract page: | 163 | Full-text PDF : | 47 | References: | 35 |
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