Abelian- and Tauberian-type results for the directional short-time fractional Fourier transform with fixed direction

Abstract

We introduce the short-time fractional Fourier transform (STFRFT) in the direction of $\vu$. Then, following the duality approach, we develop a distributional framework for the STFRFT in the direction of u on the space of Schwartz tempered distributions $\mathcal{S}'(\mathbb{R}^n)$.
We provide several Abelian- and Tauberian-type results that characterize the quasiasymptotic behavior of tempered distributions at the origin in terms of the asymptotic behavior of their STFRFT in the direction of u