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This paper provides a brief overview of the main results on the directional short-time fractional Fourier transform (DSTFRFT) defined and analyzed from Ferizi et al. (J Pseudo-Differ Oper Appl 15(63) (2024)). This new transform is a directional-sensitive variant of the short-time fractional Fourier transform (STFRFT). We provide the Parseval identity and the reconstruction formula for the DSTFRFT, along with the continuity results for the DSTFRFT and its synthesis operator on Schwartz test function spaces. Then, we define the DSTFRFT and its synthesis operator for the Schwartz-type distributions as transposes of the DSTFRFT and its synthesis operator, respectively. Furthermore, we provide an important relation between the DSTFRFT and the fractional Fourier transform (FRFT), which leads to a desingularization formula.

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The Directional Short-Time Fractional Fourier Transform of Schwartz Test Functions and Distributions

  • 会议论文

  • 发表日期：

    2026年

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  • Astrit Ferizi,
  • Katerina Hadzi-Velkova Saneva

摘要

This paper provides a brief overview of the main results on the directional short-time fractional Fourier transform (DSTFRFT) defined and analyzed from Ferizi et al. (J Pseudo-Differ Oper Appl 15(63) (2024)). This new transform is a directional-sensitive variant of the short-time fractional Fourier transform (STFRFT). We provide the Parseval identity and the reconstruction formula for the DSTFRFT, along with the continuity results for the DSTFRFT and its synthesis operator on Schwartz test function spaces. Then, we define the DSTFRFT and its synthesis operator for the Schwartz-type distributions as transposes of the DSTFRFT and its synthesis operator, respectively. Furthermore, we provide an important relation between the DSTFRFT and the fractional Fourier transform (FRFT), which leads to a desingularization formula.