On the Hermite expansions of functions from the Hardy class

Rahul Garg, and Sundaram Thangavelu. "On the Hermite expansions of functions from the Hardy class." Studia Mathematica 198.2 (2010): 177-195. <http://eudml.org/doc/285819>.

@article{RahulGarg2010,
abstract = {Considering functions f on ℝⁿ for which both f and f̂ 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 a one-dimensional result of Vemuri.},
author = {Rahul Garg, Sundaram Thangavelu},
journal = {Studia Mathematica},
keywords = {Bargmann transform; Hermite functions; Fourier-Wigner transform; Laguerre functions},
language = {eng},
number = {2},
pages = {177-195},
title = {On the Hermite expansions of functions from the Hardy class},
url = {http://eudml.org/doc/285819},
volume = {198},
year = {2010},
}

TY - JOUR
AU - Rahul Garg
AU - Sundaram Thangavelu
TI - On the Hermite expansions of functions from the Hardy class
JO - Studia Mathematica
PY - 2010
VL - 198
IS - 2
SP - 177
EP - 195
AB - Considering functions f on ℝⁿ for which both f and f̂ 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 a one-dimensional result of Vemuri.
LA - eng
KW - Bargmann transform; Hermite functions; Fourier-Wigner transform; Laguerre functions
UR - http://eudml.org/doc/285819
ER -