Abstract
The aim of this letter is to show that uncertainty principles for the pair \(u,{\mathcal F}[u]\) (\({\mathcal F}\) the Fourier transform) can be transferred without much effort to the pair \({\mathcal F}_\alpha [u],{\mathcal F}_\beta [u]\) (\({\mathcal F}_\alpha \) the Fractional Fourier transform) provided \(\beta -\alpha \notin \pi {\mathbb {Z}}\). This letter is essentially of a tutorial nature and aims at avoiding that people waste their efforts on adaptations of the proofs from classical Fourier analysis to the fractional setting.
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Communicated by Veluma Thangavelu.
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Jaming, P. A Simple Observation on the Uncertainty Principle for the Fractional Fourier Transform. J Fourier Anal Appl 28, 51 (2022). https://doi.org/10.1007/s00041-022-09946-2
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DOI: https://doi.org/10.1007/s00041-022-09946-2