分布的定向短时分数傅里叶变换

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-08-26 DOI:10.1007/s11868-024-00637-8

Astrit Ferizi, Katerina Hadzi-Velkova Saneva, Snježana Maksimović

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引用次数: 0

摘要

我们引入了定向短时分数傅里叶变换 (DSTFRFT)，并证明了其扩展的帕瑟瓦尔特性和重构公式。我们还研究了定向短时分数傅里叶变换及其合成算子在适当测试函数空间上的连续性。利用所得到的连续性结果，我们在调和分布空间 \(\mathcal {S}'(\mathbb {R}^n)\)上为 DSTFRFT 建立了一个分布框架。文章的最后，我们给出了一个去周期化公式。

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The directional short-time fractional Fourier transform of distributions

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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来源期刊

Journal of Pseudo-Differential Operators and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.20

自引率

9.10%

发文量

期刊介绍： The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.