Approximating with Gaussians

Details Approximating with Gaussians Approximating with Gaussians

2008-05-25

arxiv.org/abs/0805.3795v1

Mathematics

Classical Analysis and ODEs

16 pages, 23 figures

Scientific paper

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.

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