The two-sided quaternion Fourier transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Beurling’s theorem, Hardy, Cowling–Price and Gelfand–Shilov theorems, is obtained for the two-sided quaternion Fourier transform.

中文翻译：

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四元数傅立叶变换的贝林定理

双面四元数傅立叶变换满足一些与欧几里德傅立叶变换相似的不确定性原理。对于双面四元数傅里叶变换，获得了贝林定理的推广，哈代，考林-普莱斯和盖尔芬-希洛夫定理。