A fractal uncertainty principle for the short-time Fourier transform and Gabor multipliers
Peer reviewed, Journal article
Published version
Date
2023Metadata
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- Institutt for matematiske fag [2474]
- Publikasjoner fra CRIStin - NTNU [38289]
Original version
Applied and Computational Harmonic Analysis. 2023, 62 365-389. 10.1016/j.acha.2022.10.001Abstract
We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be formulated in terms of projection operators on the Bargmann-Fock spaces of entire functions. Specifically for signals in , we obtain norm estimates for Daubechies' time-frequency localization operator localizing on porous sets. The proof is based on the maximal Nyquist density of such sets, which we also use to derive explicit upper bound asymptotes for the multidimensional Cantor iterates, in particular. Finally, we translate the fractal uncertainty principle to discrete Gaussian Gabor multipliers.