On the Hermite expansions of functions from Hardy class

Details On the Hermite expansions of functions from Hardy class On the Hermite expansions of functions from Hardy class

2009-08-03

arxiv.org/abs/0908.0262v1

Mathematics

Classical Analysis and ODEs

22 pages

Scientific paper

Considering functions $ f $ on $ \R^n $ for which both $ f $ and $ \hat{f} $
are bounded by the Gaussian $ e^{-{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 the one dimensional result of
Vemuri.

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