TITLE:
Weinstein Gabor Transform and Applications
AUTHORS:
Hatem Mejjaoli, Ahmedou Ould Ahmed Salem
KEYWORDS:
Weinstein Gabor Transform; Practical Real Inversion Formula; Kernel Reproducing Theory
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.3,
May
29,
2012
ABSTRACT: In this paper we consider Weinstein operator. We define and study the continuous Gabor transform associated with this operator. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, we obtain analogous of Heisenberg’s inequality for the generalized continuous Gabor transform. At the end we give the practical real inversion formula for the generalized continuous Gabor transform.