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

被引：1
|
作者：
Bouzeffour, Fethi [1 ]
机构：
[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2013年 / 9卷
关键词：
special functions; differential-difference operators; integral transforms;
D O I：
10.3842/SIGMA.2013.064
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce a new differential-difference operator T-xi (xi is an element of 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 derivative(xi). In the case of one variable, we prove that the Kummer functions are eigenfunctions of this operator.
引用
收藏
页数：14
相关论文
共 25 条
  • [1] The generalized Fokker-Planck equation in terms of Dunkl-type derivatives
    Mota, R. D.
    Ojeda-Guillen, D.
    Xicotencatl, M. A.
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2024, 635
  • [2] A representation of unitary operators in Πκ in terms of isometric operators and orthogonal projections
    Muhamed Borogovac
    Acta Scientiarum Mathematicarum, 2011, 77 (3-4): : 551 - 565
  • [3] Uncertainty principles for the generalized Fourier transform associated to a Dunkl-type operator
    Mejjaoli, Hatem
    APPLICABLE ANALYSIS, 2016, 95 (09) : 1930 - 1956
  • [4] Paley–Wiener Theorem for a Generalized Fourier Transform Associated to a Dunkl-Type Operator
    Minggang Fei
    Lan Yang
    Mediterranean Journal of Mathematics, 2021, 18
  • [5] Dunkl-type generalization of the second kind beta operators via (p,q)-calculus
    Nasiruzzaman, Md.
    Alotaibi, Abdullah
    Mursaleen, M.
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2021, 2021 (01):
  • [6] A representation of unitary operators in Pi(kappa) in terms of isometric operators and orthogonal projections
    Borogovac, Muhamed
    ACTA SCIENTIARUM MATHEMATICARUM, 2011, 77 (3-4): : 551 - 565
  • [7] A Dunkl-Type Generalization of Szasz-Kantorovich Operators via Post-Quantum Calculus
    Nasiruzzaman, Md
    Mukheimer, Aiman
    Mursaleen, M.
    SYMMETRY-BASEL, 2019, 11 (02):
  • [8] Paley-Wiener Theorem for a Generalized Fourier Transform Associated to a Dunkl-Type Operator
    Fei, Minggang
    Yang, Lan
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (05)
  • [9] Approximation of Functions by Dunkl-Type Generalization of Szasz-Durrmeyer Operators Based on (p, q)-Integers
    Alotaibi, Abdullah
    JOURNAL OF FUNCTION SPACES, 2021, 2021
  • [10] Approximation by a Class of q-Beta Operators of the Second Kind Via the Dunkl-Type Generalization on Weighted Spaces
    Srivastava, H. M.
    Mursaleen, M.
    Nasiruzzaman, Md.
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2019, 13 (03) : 1537 - 1556
123