与双边四元数傅里叶变换有关的Benedicks-Amrein-Berthier型定理
Benedicks-Amrein-Berthier type theorem related to the two-sided Quaternion Fourier transform
摘要：
本文的主要目的是建立双边四元数傅里叶变换（QFT）的一个新的测不准原理（UP）。这个结果推广了Benedicks，Amrein和Berthier的一个结果，即$L^1\left({\mathbb{R}}^2, {\mathbb{H}}\right)$中的非零函数和它的双边QFT不可能都有有限测度的支持.
英文摘要：
The main objective of the present paper is to establish a new uncertainty principle (UP) for the two-sided quaternion Fourier transform (QFT). This result is an extension of a result of Benedicks, Amrein and Berthier, which states that a nonzero function in $L^1\left({\mathbb{R}}^2, {\mathbb{H}}\right)$ and its two-sided QFT cannot both have support of finite measure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
