Abstract: “In this work, we establish Heisenberg-type uncertainty principle for the Dunkl-type Fock space ( ) d k F C . Next, we give an application of the classical theory of reproducing kernels to the Tikhonov regularization problem for operator L F C H d k : ( ) , where H be a Hilbert space. Finally, we come up with some results regarding the Tikhonov regularization problem and the Heisenberg-type uncertainty principle for the Dunkl-type Segal-Bargmann transform k B .”

Keywords: component, Dunkl-type Fock spaces, extremal functions, Tikhonov regularization, Heisenberg-type uncertainty principle.