On pair correlation of Hermite coefficients of functions from the Hardy class

Abstract

Assuming that a function and its Fourier transform are dominated by a Gaussian, Vemuri found a sharp estimate for the decay rate of the Hermite coefficients in terms of the variance of the dominating Gaussian. Here we show that under the same assumptions, certain combinations of Hermite coefficients have a better rate of decay. © The Author(s), under exclusive licence to The Forum D’Analystes 2024.