Geodesic
On the Hermite expansions of functions from the Hardy class
Rahul Garg 1   ; Sundaram Thangavelu 1
1 Department of Mathematics Indian Institute of Science Bangalore 560 012, India
Studia Mathematica, Tome 198 (2010) no. 2, pp. 177-195 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm198-2-5
Keywords: considering functions mathbb which hat bounded gaussian frac their fourier hermite coefficients have exponential decay optimal decay obtained finite functions extending one dimensional result vemuri

Rahul Garg  1   ; Sundaram Thangavelu  1

1 Department of Mathematics Indian Institute of Science Bangalore 560 012, India 
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Rahul Garg; Sundaram Thangavelu. On the Hermite expansions of functions
from the Hardy class. Studia Mathematica, Tome 198 (2010) no. 2, pp. 177-195. doi: 10.4064/sm198-2-5

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