Geodesic
Dunkl-Type Operators with Projections Terms Associated to Orthogonal Subsystems in Roots System
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2013_9_a63,
     author = {Fethi Bouzeffour},
     title = {Dunkl-Type {Operators} with {Projections} {Terms} {Associated} to {Orthogonal} {Subsystems} in {Roots} {System}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2013},
     volume = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a63/}
}
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Fethi Bouzeffour. Dunkl-Type Operators with Projections Terms Associated to Orthogonal Subsystems in Roots System. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a63/

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