Hypergeometric Gabor transform and uncertainty principles (Q6614725)

In this contribution the author proposes the hypergeometric Gabor transform as an extension of the classical Gabor transform within the Heckman-Opdam theoretical framework. This extension adapts the Gabor methodology to the setting of hypergeometric Fourier transforms associated with Cherednik operators. Also, the author extends classical uncertainty principles to the hypergeometric Gabor setting. It includes quantitative Heisenberg-type inequalities, entropy-based uncertainty principle, and localization results, such as Benedicks-type principles and Donoho-Stark inequalities. Finally, a framework for further exploration is given.