DIFFERENCE AND PRIMITIVE OPERATORS ON THE DUNKL-TYPE FOCK SPACE $$\mathscr {F}_{\alpha }(\mathbb {C}^{d})$$

In 1961, Bargmann introduced the classical Fock space $$\mathscr {F}(\mathbb {C}^{d})$$ and in 1984, Cholewinsky generalized {F}_{\alpha ,e}(\mathbb . These two spaces are aim of many works, have applications mathematics, physics, quantum mechanics. this work, we introduce study }(\mathbb associated to Dunkl operators $$T_{\alpha _{j}}$$ with $$\alpha _{j}>-1/2$$ for all $$j=1,\ldots ,d$$ This is an extension Dunkl-type {C})$$ constructed by Sifi Soltani 2002. We prove that a Hilbert reproducing kernel. Next, give application theory kernels Tikhonov regularization problem bounded linear operator {L}:\mathscr {C}^{d})\rightarrow \mathscr {H}$$ , where space. Finally, come up some results regarding extremal functions, when {L}$$ difference primitive operator, respectively.