  Spherical Gauss-Laguerre (SGL) basis functions, i. e., normalized functions
of the type $L_{n-l-1}^{(l + 1/2)}(r^2) r^l Y_{lm}(\vartheta,\varphi)$, $|m|
\leq l < n \in \mathbb{N}$, $L_{n-l-1}^{(l + 1/2)}$ being a generalized
Laguerre polynomial, $Y_{lm}$ a spherical harmonic, constitute an orthonormal
polynomial basis of the space $L^2$ on $\mathbb{R}^3$ 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 $\mathbb{R}^3$. 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 proof an error
estimate for our algorithms and validate their practical suitability in
extensive numerical experiments.
