q-Hankel-Stockwell变换的不确定性原理

Ukrains’kyi Matematychnyi Zhurnal Pub Date : 2023-07-25 DOI:10.37863/umzh.v75i7.7166

K. Brahim, Hédi Ben Elmonser

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引用次数: 0

摘要

利用q-Jackson积分和与q-Hankel变换相关的q-harmonic分析的一些元素，引入并研究了Hankel-Stockwell变换的q-类比。给出了一些谐波分析性质(Plancherel公式、反演公式、再现核等)。此外，我们建立了海森堡测不准原理的一个版本。最后，研究了有限测度子集上的q-Hankel-Stockwell变换。

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Uncertainty principles for the q -Hankel–Stockwell transform

UDC 517.3 By using the q -Jackson integral and some elements of the q -harmonic analysis associated with the q -Hankel transform, we introduce and study a q -analog of the Hankel–Stockwell transform. We give some harmonic analysis properties (Plancherel formula, inversion formula, reproduicing kernel, etc.). Furthermore, we establish a version of Heisenberg's uncertainty principles. Finally, we study the q -Hankel–Stockwell transform on a subset of finite measure.

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Ukrains’kyi Matematychnyi Zhurnal

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