On the Hermite expansions of functions from the Hardy class
Volume 198 / 2010
Studia Mathematica 198 (2010), 177-195
MSC: Primary 42C15; Secondary 42B35, 42C10, 42A56.
DOI: 10.4064/sm198-2-5
Abstract
Considering functions $ f $ on $ \mathbb R^n $ for which both $ f $ and $ \hat{f} $ are bounded by the Gaussian $ e^{-\frac{1}{2}a|x|^2} , 0 < a < 1 $, we show that their Fourier–Hermite coefficients have exponential decay. Optimal decay is obtained for $ O(n)$-finite functions, thus extending a one-dimensional result of Vemuri.
