The directional short-time fractional Fourier transform of distributions
Astrit Ferizi, Katerina Hadzi-Velkova Saneva, Snjezana Maksimovic
公開日: 2024/7/21
Abstract
We introduce the directional short-time fractional Fourier transform (DSTFRFT) and prove an extended Parseval's identity and a reconstruction formula for it. We also investigate the continuity of both the directional short-time fractional Fourier transform and its synthesis operator on the appropriate space of test functions. Using the obtained continuity results, we develop a distributional framework for the DSTFRFT on the space of tempered distributions $\mathcal{S}'(\mathbb{R}^n)$. We end the article with a desingularization formula.