Volume 52, pp. 249-269, 2020.

Approximation of Gaussians by spherical Gauss-Laguerre basis in the weighted Hilbert space

Nadiia Derevianko and Jürgen Prestin

Abstract

This paper is devoted to the study of approximation of Gaussian functions by their partial Fourier sums of degree $N\in \mathbb{N}$ with respect to the spherical Gauss-Laguerre (SGL) basis in the weighted Hilbert space $L_2({\mathbb{R}}^3,{\omega }_{\lambda })$, where ${\omega }_{\lambda }(|\mathit{x}|)=\exp (-|\mathit{x}{|}^2/\lambda )$, $\lambda >0$. We investigate the behavior of the corresponding error of approximation with respect to the scale factor $\lambda$ 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 $L_2({\mathbb{R}}^3,{\omega }_{\lambda })$. Possible application of obtained results to the docking problem are described.

Full Text (PDF) [480 KB], BibTeX , DOI: 10.1553/etna_vol52s249

Key words

spherical harmonic, Laguerre polynomial, Gaussian, hypergeometric function, molecular docking

AMS subject classifications

33C05, 33C45, 33C55, 42C10