Inversion theorem and quantitative uncertainty principles for the Dunkl Gabor transform on $${\mathbb {R}}^{d}$$ R d

Abstract

We prove a new inversion formula for the Dunkl Gabor transform. We also prove several versions of Heisenberg-type inequalities, Donoho–Stark’s uncertainty principles, local Cowling–Price’s type inequalities and finally Faris–Price’s uncertainty principle for the previous transform.