Abstract
In this paper, we present a set of important properties of the special relativistic Fourier transformation (SFT) on the complex space–time algebra \({\mathcal {G}}{(3,1)}\), such as inversion property, the Plancherel theorem, and the Hausdorff–Young inequality. The main objective of this article is to introduce the concept of the vector derivative in geometric algebra and using it together with the notion of the space–time split to derive the Heisenberg–Pauli–Weyl inequality. Finally, we apply the SFT properties for proving the Donoho–Stark uncertainty principle for \({\mathcal {G}}{(3,1)}\) multi-vector functions.
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The author is grateful to the editor and the two anonymous referees, whose insightful comments improved the paper immensely.
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El Haoui, Y. Uncertainty Principle for Space–Time Algebra-Valued Functions. Mediterr. J. Math. 18, 97 (2021). https://doi.org/10.1007/s00009-021-01718-4
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DOI: https://doi.org/10.1007/s00009-021-01718-4