Multiplication and Translation Operators on the Fock Spaces for the q-Modified Bessel Function

Abstract

We study the multiplication operator <i>M</i> by <i>z</i>² and the <i>q</i>-Bessel operator Δ_<i>q,α</i>on a Hilbert spaces F_<i>q,α</i> of entire functions on the disk D( o, ) , 0<<i>q</i><1 ; and we prove that these operators are adjoint-operators and continuous from F_<i>q,α</i> into itself. Next, we study a generalized translation operators on F_<i>q,α</i> .