Approximation of gaussians by spherical gauss-laguerre basis in the weighted hilbert space

This paper is devoted to the study of approximation of Gaussian functions by their partial Fourier sums of degree N ∈ N with respect to the spherical Gauss-Laguerre (SGL) basis in the weighted Hilbert space L₂(R³, ω_λ), where ω_λ(|x|) = exp(−|x|²/λ), λ > 0. We investigate the behavior of the corresponding error of approximation with respect to the scale factor λ and order of expansion N. As interim results we obtained formulas for the Fourier coefficients of Gaussians with respect to SGL basis in the space L₂(R³, ω_λ). Possible application of obtained results to the docking problem are described.