On the Hermite expansions of functions from the Hardy class
Rahul Garg ; Sundaram Thangavelu
Studia Mathematica, Tome 196 (2010), p. 177-195 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Considering functions f on ℝⁿ for which both f and f̂ 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 a one-dimensional result of Vemuri.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:285819 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-2-5,
     author = {Rahul Garg and Sundaram Thangavelu},
     title = {On the Hermite expansions of functions from the Hardy class},
     journal = {Studia Mathematica},
     volume = {196},
     year = {2010},
     pages = {177-195},
     zbl = {1198.42029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-2-5}
}

Rahul Garg; Sundaram Thangavelu. On the Hermite expansions of functions from the Hardy class. Studia Mathematica, Tome 196 (2010) pp. 177-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-2-5/