Hypercyclic and Chaotic Convolution Associated with the Jacobi–Dunkl Operator

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 operat...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 11; no. 2; pp. 577 - 600
Main Authors Chouchene, F., Mejjaoli, H., Mili, M., Trimèche, K.
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.05.2014
Subjects
Mathematics
Mathematics and Statistics
OriginalPaper
46F12
42A85
46E10
47A16
44A35
convolution
Jacobi–Dunkl operator
hypercyclic and chaotic operators
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Summary: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.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-013-0301-1