In this research, the Clifford–Fourier transform introduced by E. Hitzer, satisfies some uncertainty principles similar to the Euclidean Fourier transform. An analog of the Beurling–Hörmander’s theorem for the Clifford–Fourier transform is obtained. As a straightforward consequence of Beurling’s theorem, other versions of the uncertainty principle, such as the Hardy, Gelfand–Shilov and Cowling–Price theorems are also deduced.

中文翻译：

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克利福德代数中的伯林定理

在本研究中，E. Hitzer 提出的克利福德-傅里叶变换满足一些类似于欧几里德傅里叶变换的不确定性原理。获得了 Clifford-Fourier 变换的 Beurling-Hörmander 定理的模拟。作为 Beurling 定理的直接推论，不确定性原理的其他版本，例如 Hardy、Gelfand-Shilov 和 Cowling-Price 定理也被推导出来。