Abstract
In this work, the space–time Fourier transform SFT introduced by E. Hitzer satisfies some uncertainty principles of the algebra for space–time \( Cl_{(3,1)} \)-valued signals over the space–time vector space \( {\mathbb {R}}^{(3,1)} \). An analog of the Beurling theorem for the SFT is obtained. As a direct consequence of Beurling’s theorem, other versions of the uncertainty principle, such as Hardy’s, Gelfand–Shilov’s, Cowling–Price’s and Morgan’s theorems are also deduced.
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Tyr, O., Daher, R. The Beurling Theorem in Space–Time Algebras. Bull. Malays. Math. Sci. Soc. 46, 176 (2023). https://doi.org/10.1007/s40840-023-01571-6
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DOI: https://doi.org/10.1007/s40840-023-01571-6