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Fock Spaces for the q-Dunkl Kernel
Higher College of Technology and Informatics, Tunis, Tunisia
- 1 Higher College of Technology and Informatics, Tunis, Tunisia
Advances in Pure Mathematics·Volume 02 (2012)·Pages 169–176·Published 29 May 2012·DOI10.4236/apm.2012.23023
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Abstract
In this work, we introduce a class of Hilbert spaces of entire functions on the disk , 0＜q＜1 , with reproducing kernel given by the q-Dunkl kernel . The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Q by z and the q-Dunkl operator on the Fock space ; and we prove that these operators are adjoint-operators and continuous from this space into itself.
KeywordsGeneralized q-Fock Spacesq-Dunkl Kernelq-Dunkl Operatorq-Translation Operators
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