Mathematics – Classical Analysis and ODEs
Scientific paper
2008-05-25
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.
Boldt Axel
Calcaterra Craig
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