On the Hermite expansions of functions from Hardy class

Rahul Garg, Sundaram Thangavelu

Considering functions $f$ on ${\mathbb{R}}^n$ for which both $f$ and $\hat{f}$ are bounded by the Gaussian $e^{-1/2a|x{|}^2},0<a<1$ we show that their Fourier-Hermite coeffici…