We introduce a continuous k-Hankel Gabor transform acting on a Hilbert space deforming \(L^2(\mathbb R)\). We prove a Plancherel formula and \(L^2\)-inversion formulas for it. We also prove several uncertainty principles for this transform such as Heisenberg type inequalities and Faris–Price type uncertainty principle.

中文翻译：

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与k-Hankel Gabor变换有关的谐波分析问题

我们介绍了作用于希尔伯特空间变形\（L ^ 2（\ mathbb R）\）的连续k- Hankel Gabor变换。我们证明了Plancherel公式和\（L ^ 2 \）-反演公式。我们还证明了此变换的几种不确定性原理，例如海森堡类型不等式和法里斯-普莱斯类型不确定性原理。