Uncertainty principles for the q -Hankel–Stockwell transform

Abstract

UDC 517.3 By using the q -Jackson integral and some elements of the q -harmonic analysis associated with the q -Hankel transform, we introduce and study a q -analog of the Hankel–Stockwell transform. We give some harmonic analysis properties (Plancherel formula, inversion formula, reproduicing kernel, etc.). Furthermore, we establish a version of Heisenberg's uncertainty principles. Finally, we study the q -Hankel–Stockwell transform on a subset of finite measure.