Fast SGL Fourier transforms for scattered data

Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type L-n-l-1((l+1/2)) (r(2))r(l)Y(lm) (theta, phi), vertical bar m vertical bar <= l < n is an element of N, L-n-l-1((l+1/2)) being a generalized Laguerre polynomial, Y-lm a spherical harmonic, constitute an orthonormal polynom- ial basis of the space L-2 on R-3 with radial Gaussian (multivariate Hermite) weight exp(-r(2)). We have recently described fast Fourier transforms for the SGL basis functions based on an exact quadrature formula with certain grid points in R-3. In this paper, we present fast SGL Fourier transforms for scattered data. The idea is to employ well-known basal fast algorithms to determine a three-dimensional trigonometric polynomial that coincides with the bandlimited function of interest where the latter is to be evaluated. This trigonometric polynomial can then be evaluated efficiently using the well-known non-equispaced FFT (NFFT). We prove an error estimate for our algorithms and validate their practical suitability in extensive numerical experiments. (C) 2019 Elsevier Inc. All rights reserved.