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arXiv · 2407.15135

The directional short-time fractional Fourier transform of distributions

Astrit Ferizi·Katerina Hadzi-Velkova Saneva·Snjezana Maksimovic
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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.

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Astrit Ferizi, Katerina Hadzi-Velkova Saneva, Snjezana Maksimovic. 2024-07-21. The directional short-time fractional Fourier transform of distributions. https://doi.org/10.1007/s11868-024-00637-8

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