A fractal uncertainty principle for the short-time Fourier transform and Gabor multipliers

We study the fractal uncertainty principle in joint time-frequency representation, and we prove a version for Short-Time Fourier transform with Gaussian window on modulation spaces. This can equivalently be formulated terms of projection operators Bargmann-Fock spaces entire functions. Specifically signals L 2 ( R d ) , obtain norm estimates Daubechies' localization operator localizing porous sets. The proof is based maximal Nyquist density such sets, which also use to derive explicit upper bound asymptotes multidimensional Cantor iterates, particular. Finally, translate discrete Gabor multipliers.