Approximating with Gaussians
Classical Analysis and ODEs
2008-05-27 v1 Functional Analysis
Abstract
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.
Cite
@article{arxiv.0805.3795,
title = {Approximating with Gaussians},
author = {Craig Calcaterra and Axel Boldt},
journal= {arXiv preprint arXiv:0805.3795},
year = {2008}
}
Comments
16 pages, 23 figures