Approximating with Gaussians

Mathematics – Classical Analysis and ODEs

Scientific paper

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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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