Uncertainty Principles and Calderón’s Formula for the Multidimensional Hankel-Gabor Transform

Abstract

The main crux of this paper is to introduce a new integral transform called the multidimensional Hankel-Gabor transform and to give some new results related to this transform as Plancherel’s, Parseval’s, inversion and Calderón’s reproducing formulas. Next, we analyse the concentration of this transform on sets of finite measure and we give uncertainty principle for orthonormal sequences. Last, we extend the Donoho-Stark’s uncertainty principle to the multidimensional Hankel-Gabor setting.