A Fractal Uncertainty Principle for the Short-Time Fourier Transform and Gabor Multipliers
A Fractal Uncertainty Principle for the Short-Time Fourier Transform and Gabor Multipliers
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 $L^2(\mathbb{R}^d)$, …