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H. Mejjaoli and N. Sraieb, “Gabor Transform in Quantum Calculus and Applications,” Fractional Calculus and Applied Analysis, Vol. 12, No. 3, 2009, pp. 320-336.

has been cited by the following article:

• 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.