Voronoi-Hankel Transforms

Let $π$ be a generic irreducible representation of $\mathrm{GL}_n(\mathbf{F})$ for a local field $\mathbf{F}$. We introduce the Voronoi--Hankel transform $\mathcal{VH}_π$ for $π$, and prove it is equivalent to the $π$-Fourier transform introduced by Jiang--Luo. We give an extension $\widetilde{\math