Speaker: Shuang Guan, Tufts University

Date: September 30, 2025

Abstract: We investigate uniqueness sets on the real line for L^2 functions whose Fourier transforms exhibit super-exponential decay. Such functions can be analytically extended to entire functions of a specified order ρ>1. We establish two results concerning the density of their zeros. This theoretical framework generalizes existing results for the 2nd order case (ρ=2) to any order ρ>1. Finally, we apply these findings to the Short-Time Fourier Transform (STFT) phase retrieval problem, demonstrating that if the window function belongs to this class, uniqueness of a signal can be guaranteed from its STFT intensity measurements on a sufficiently dense ρ-root lattice.