Hypercyclic and Chaotic Convolution Associated with the Jacobi–Dunkl Operator

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• 作者：F. Chouchene (1)
  H. Mejjaoli (2)
  M. Mili (1)
  K. Trimèche (3)
  
• 关键词：42A85 ; 44A35 ; 46E10 ; 46F12 ; 47A16 ; Jacobi–Dunkl operator ; convolution ; hypercyclic and chaotic operators
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：11
• 期：2
• 页码：577-600
• 全文大小：
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• 作者单位：F. Chouchene (1)
  H. Mejjaoli (2)
  M. Mili (1)
  K. Trimèche (3)
  
  1. Department of Mathematics, Faculty of Sciences of Monastir, 5019, Monastir, Tunisia
  2. Department of Mathematics, College of Sciences, Taibah University, Po Box 30002, Al Madinah, AL Munawarah, Saudi Arabia
  3. Faculty of Sciences of Tunis, Department of Mathematics, CAMPUS, 2092, Tunis, Tunisia
  
• ISSN：1660-5454

文摘

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.