Using the basic properties of the Gelfand pairs and its spherical Fourier transform, we introduce the spherical Gabor transform. We show its fundamental properties, such as Plancherel, Parseval and inversion formula. Finally, we establish a number of uncertainty principles (such as Donoho–Stark’s uncertainty principle , Lieb inequality and Beckner’s uncertainty principle ) associated with this transformation.

中文翻译：

---

Gelfand对的连续球面Gabor变换

利用Gelfand对的基本特性及其球傅立叶变换，我们介绍了球Gabor变换。我们将展示其基本属性，例如Plancherel，Parseval和反演公式。最后，我们建立了与此转换相关的许多不确定性原理（例如Donoho–Stark的不确定性原理，Lieb不等式和Beckner的不确定性原理）。