Approximating with Gaussians
Abstract
Description
Linear 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 figures
16 pages, 23 figures