Abstract
In this paper, we investigate the k-Hankel Gabor transform on R-d in some problems of time-frequency analysis. Firstly, we present the main theorems of Harmonic analysis as Plancherel's, Lieb's and inversion formulas for this transform. Next, we formulate some novel uncertainty principles including the Heisenberg and logarithmic uncertainty principles, Benedick-Amrein-Berthier's uncertainty principle, local uncertainty principles and Shapiro's uncertainty principle. In sequel, we introduce the localization operators associated with the k-Hankel Gabor transform on R-d and we develop corresponding theory. In particular we study their trace class properties and we prove that they are in the Schatten-von Neumann.