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 aback ground to our contribution. Especially, we study themultiplication 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. 2020 Mathematics Subject Classification: 30H20, 32A15