Uncertainty Principles for the q-Hankel–Stockwell Transform

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 present some properties from harmonic analysis (Plancherel formula, inversion formula, reproducing 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.