Benedicks-Amrein-Berthier type theorem related to the two-sided Quaternion Fourier transform

Abstract

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.

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