Abstract
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.
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Tyr, O., Daher, R. Beurling’s Theorem in the Clifford Algebras. Adv. Appl. Clifford Algebras 33, 37 (2023). https://doi.org/10.1007/s00006-023-01284-w
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DOI: https://doi.org/10.1007/s00006-023-01284-w