Uncertainty principles for the q-bessel fourier transform

Abstract

ABSTRACTThe aim of this paper is to continue the study of the uncertainty principle to the q-Bessel Fourier transform , that began in [Dhaouadi L. Heisenberg uncertainty principle for the q-Bessel Fourier transform. Preprint; 2007; Dhaouadi L. On the q-Bessel Fourier transform. Bull Math Anal Appl. 2013;5(2):42–60; Hleili M, Nefzi B, Bsaissa A. A variation on uncertainty principles for the generalized q-Bessel Fourier transform. J Math Anal Appl. 2016;440:823–832]. More precisely, we show an extension of Faris's local uncertainty principle and a general form of Heisenberg-type uncertainty inequality for on the space . We also prove new uncertainty principles for on the subspaces of functions that are essentially concentrated on S and bandlimited on Σ, or functions that are essentially timelimited on S and bandlimited on Σ, where S and Σ are general subsets of finite measure.