Hypercyclic and Chaotic Convolution Associated with the Jacobi-Dunkl Operator

被引：2

作者：

Chouchene, F. ^{[1
]}

Mejjaoli, H. ^{[2
]}

Mili, M. ^{[1
]}

Trimeche, K. ^{[3
]}

机构：

[1] Fac Sci Monastir, Dept Math, Monastir 5019, Tunisia

[2] Taibah Univ, Dept Math, Coll Sci, Al Madinah, Al Munawarah, Saudi Arabia

[3] Fac Sci Tunis, Dept Math, Tunis 2092, Tunisia

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2014年 / 11卷 / 02期

关键词：

Jacobi-Dunkl operator; convolution; hypercyclic and chaotic operators; DIFFERENTIAL-DIFFERENCE OPERATOR; TRANSMUTATION OPERATORS; REAL LINE; THEOREM;

D O I：

10.1007/s00009-013-0301-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the Jacobi-Dunkl convolution operators on some distribution spaces. We characterize the Jacobi-Dunkl convolution operators as those ones that commute with the Jacobi-Dunkl translations and with the Jacobi-Dunkl operators. Also we prove that the Jacobi-Dunkl convolution operators are hypercyclic and chaotic on the spaces under consideration and we give a universality property for the generalized heat equation associated with them.

引用

页码：577 / 600

页数：24

共 36 条

[1] Hypercyclic and Chaotic Convolution Associated with the Jacobi–Dunkl Operator
F. Chouchene
H. Mejjaoli
M. Mili
K. Trimèche
Mediterranean Journal of Mathematics, 2014, 11 : 577 - 600
[2] Convolution structure associated with the Jacobi-Dunkl operator on IR
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[3] Convolution structure associated with the Jacobi-Dunkl operator on IR
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[4] Hypercyclic and chaotic convolution operators associated with the Dunkl operator on C
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[5] Generalized Wigner transform associated with the Jacobi-Dunkl operator and uncertainty principles
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[7] Hypoelliptic Jacobi-Dunkl convolution of distributions
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[8] Hypercyclic and chaotic convolution operators associated with the Dunkl operator on <Emphasis Type=”Bold”>C</Emphasis>
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Acta Mathematica Hungarica, 2005, 106 : 101 - 116
[9] The heat semigroup for the Jacobi-Dunkl operator and the related Markov processes
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[10] The Jacobi-Dunkl transform on R and the convolution product on new spaces of distributions
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