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Fock Spaces for the q-Dunkl Kernel

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DOI: 10.4236/apm.2012.23023    3,171 Downloads   6,384 Views   Citations
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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.

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The authors declare no conflicts of interest.

Cite this paper

F. Soltani, "Fock Spaces for the q-Dunkl Kernel," Advances in Pure Mathematics, Vol. 2 No. 3, 2012, pp. 169-176. doi: 10.4236/apm.2012.23023.


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