Approximation of Gaussians by spherical Gauss-Laguerre basis in the weighted Hilbert space. ETNA - Electronic Transactions on Numerical Analysis

This paper is devoted to the study of approximation of Gaussian functions bytheir partial Fourier sums of degree $N \in \mathbb{N}$ with respect to thespherical Gauss-Laguerre (SGL) basis in the weighted Hilbert space$L_2(\mathbb{R}^3, \omega_\lambda)$, where$\omega_\lambda(|\boldsymbol{x}|)=\exp({-|\boldsymbol{x}|^2/\lambda})$,$\lambda>0$. We investigate the behavior of the corresponding error ofapproximation with respect to the scale factor $\lambda$ and order ofexpansion $N$. As interim results we obtained formulas for the Fouriercoefficients of Gaussians with respect to SGL basis in the space$L_2(\mathbb{R}^3, \omega_\lambda)$. Possible application of obtained resultsto the docking problem are described