Weinstein Gabor Transform and Applications

Hatem Mejjaoli, Ahmedou Ould Ahmed Salem

Department of Mathematics, College of Education, King Khalid University, Mohayil, Kingdom of Saudi Arabia.
Department of Mathematics, College of Sciences, King Faisal University, Ahsaa, Kingdom of Saudi Arabia.

DOI: 10.4236/apm.2012.23029                

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.

Keywords

Weinstein Gabor Transform; Practical Real Inversion Formula; Kernel Reproducing Theory

Conflicts of Interest

The authors declare no conflicts of interest.

References

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