Toeplitz and Translation Operators on the q-Fock Spaces

Abstract

In this work, we introduce a class of Hilbert spaces F_q of entire functions on the disk , , with reproducing kernel given by the q-exponential function e_q(z); and we prove some properties concerning Toeplitz operators on this space. The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator D_q by and the q-Derivative operator on the Fock space F_q ; and we prove that these operators are adjoint-operators and continuous from this space into itself. Lastly, we study a generalized translation operators and a Weyl commutation relations on F_q .