Fock Spaces for the q-Dunkl Kernel

Fethi Soltani

Higher College of Technology and Informatics, Tunis, Tunisia.

DOI: 10.4236/apm.2012.23023                

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.

Keywords

Generalized q-Fock Spaces; q-Dunkl Kernel; q-Dunkl Operator; q-Translation Operators

Conflicts of Interest

The authors declare no conflicts of interest.

References

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