On the Hermite expansions of functions from Hardy class

Abstract

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 coefficients have exponential decay. Optimal decay is obtained for $O(n)-$finite functions thus extending the one dimensional result of Vemuri.

22 pages

References in corpus (1)

• Hermite expansions and Hardy's theorem

Cited by in corpus (2)

• On the structure of analytic vectors for the schrodinger representation
• Variations on a theorem of Beurling