Gabor transform in the generalized Weinstein theory setting

Abstract

In this paper, we consider the generalized Weinstein operator Δ_{W}^{d,α,n}, we introduce and study the continuous generalized Weinstein Gabor Transform denoted by G_{g} associated with the operator Δ_{W}^{d,α,n}. We prove a Plancherel formula and a weak uncertainty principle for it. We obtain analogous of Heisenbeg's inequality for the generalized Weinstein Gabor Transform.