Orlicz spaces and the uncertainty principle

Abstract

Let $f$ be a finite signal. The classical uncertainty principle tells us that the product of the support of $f$ and the support of $\hat{f}$, the Fourier transform of $f$, must satisfy $|supp(f)|\cdot|supp(\hat{f})|\geq |G|$. Recently, Iosevich and Mayeli improved the uncertainty principle for signals with Fourier supported on generic sets. This was done by employing the Fourier restriction theory in $L^p$ spaces. In this paper, we extended the $(p,q)$-restriction setting to Orlicz spaces. Then we apply uncertainty principles to the problem of exact recovery, which again extends and recovers the result that Iosevich and Mayeli obtained in Lebesgue spaces.