2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161613Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the approximations are given, using orthogonal Hermite functions and least squares. Taking the Fourier transform of this result shows low-frequency trigonometric series are dense in L^2 with Gaussian weight function.16 pages, 23 figuresClassical Analysis and ODEsFunctional Analysis41A30; 42A32; 42C10text