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Weinstein Gabor Transform and Applications

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Author(s): Hatem Mejjaoli | Ahmedou Ould Ahmed Salem

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 02;
Issue: 03;
Start page: 203;
Date: 2012;
Original page

Keywords: Weinstein Gabor Transform | Practical Real Inversion Formula | Kernel Reproducing Theory

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.
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