Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System

Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System

In this paper, we introduce a new differential-difference operator T_ξ (ξ∈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_ξ and the directional derivativ...

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Main Author: Fethi Bouzeffour
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2013-10-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
special functions
differential-difference operators
integral transforms
Online Access:http://dx.doi.org/10.3842/SIGMA.2013.064
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spelling doaj-b89e73f9a88444bd84d1c3ce78ec17042020-11-25T00:44:02ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592013-10-01906410.3842/SIGMA.2013.064Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root SystemFethi BouzeffourIn this paper, we introduce a new differential-difference operator T_ξ (ξ∈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_ξ and the directional derivative ∂_ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this operator. http://dx.doi.org/10.3842/SIGMA.2013.064special functionsdifferential-difference operatorsintegral transforms
collection DOAJ
language English
format Article
sources DOAJ
author Fethi Bouzeffour
spellingShingle Fethi Bouzeffour
Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System
Symmetry, Integrability and Geometry: Methods and Applications
special functions
differential-difference operators
integral transforms
author_facet Fethi Bouzeffour
author_sort Fethi Bouzeffour
title Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System
title_short Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System
title_full Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System
title_fullStr Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System
title_full_unstemmed Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System
title_sort dunkl-type operators with projection terms associated to orthogonal subsystems in root system
publisher National Academy of Science of Ukraine
series Symmetry, Integrability and Geometry: Methods and Applications
issn 1815-0659
publishDate 2013-10-01
description In this paper, we introduce a new differential-difference operator T_ξ (ξ∈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_ξ and the directional derivative ∂_ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this operator.
topic special functions
differential-difference operators
integral transforms
url http://dx.doi.org/10.3842/SIGMA.2013.064
work_keys_str_mv AT fethibouzeffour dunkltypeoperatorswithprojectiontermsassociatedtoorthogonalsubsystemsinrootsystem
_version_ 1725276961755889664

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