2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128261Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $\R^d$ induced by Hermite expansions can be characterized in terms of the needlet coefficients. It is also shown that the Hermite Triebel-Lizorkin and Besov spaces are, in general, different from the respective classical spaces.34 pagesClassical Analysis and ODEsFunctional Analysis42B35, 42C15text