Uncertainty inequality for weighted Fock spaces

Abstract

In this paper we introduce a weighted Fock space $\mathscr {F}_{\beta }$. This space which gives a generalization of some Hilbert spaces of analytic functions on the complex plane $\mathbb {C}$ like, the classical Fock space $\mathscr {F}$, the Dunkl type Fock space $\mathscr {F}_{\nu }$ and the Bessel-Struve type Fock space $\mathbb {F}_{\nu }$, it plays a background to our contribution. Especially, we study the multiplication operator M by $z^2$ and its adjoint operator $L_{\mathscr {F}_{\beta }}$ on $\mathscr {F}_{\beta }$, and we deduce a general uncertainty inequality of Heisenberg type for this space.