Abstract: “In this work, we introduce the Fock space F (C)  associated to the Airy operator , and we establish Heisenberg-type uncertainty principle for this space. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator T : F (C)H  , where H be a Hilbert space. Finally, we come up with some results regarding the extremal functions, when T is the difference operator and the Dunkl-difference operator, respectively”

Keywords: component, Airy-type Fock space, Tikhonov regularization, Heisenberg-type uncertainty principle.