The directional short-time fractional Fourier transform of distributions

2024/07/21 by Astrit Ferizi, Ferizi, Astrit, Katerina Saneva +3
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods

paper · doi:10.48550/arxiv.2407.15135

openalex publication_date 2024/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S'(ℝⁿ). We end the article with a desingularization formula.

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• Directional short-time Fourier transform and directional regularity
• Directional Stockwell transform of distributions
• Fourier transforms, fractional derivatives, and a little bit of quantum mechanics
• Applications of a distributional fractional derivative to Fourier analysis and its related differential equations
• Directional short-time Fourier transform of ultradistributions