Uncertainty principles for the second $q$-Bargmann transform on the unit disk
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In this paper, we give a local uncertainty principle inequality for the second $q$-Bargmann transform $\mathcal{B}_{\alpha,q}$ introduced by Essadiq et al. in \cite{Essadiq} and we derive a $q$-version of Heisenberg-type uncertainty principle on the $q$-weighted Bergman space $\mathcal{A}_{{\alpha,q}}$. Also, using this local uncertainty principle and the partial $q$-Bargmann integrals, we establish an uncertainty principle of concentration type for this transform.
Abstract
In this paper, we give a local uncertainty principle inequality for the second $q$-Bargmann transform $\mathcal{B}_{\alpha,q}$ introduced by Essadiq et al. in \cite{Essadiq} and we derive a $q$-version of Heisenberg-type uncertainty principle on the $q$-weighted Bergman space $\mathcal{A}_{{\alpha,q}}$. Also, using this local uncertainty principle and the partial $q$-Bargmann integrals, we establish an uncertainty principle of concentration type for this transform.