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• ## Forschungsschwerpunkte M.Sc. Christian Wülker

14/05/17 NEWS! The new C++ version of our fast SGL Fourier transforms is now available on Github. This version employs the fast spherical Fourier transforms of SpharmonicKit, and supports bandwidths of up to 256. You can still download the Matlab version here.

Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type $\color{black}{L_{n-l-1}^{(l + 1/2)} (r^2) r^{l} Y_{lm}(\vartheta,\varphi)}$, $\color{black}{|m| \leq l \leq n \in \mathbb{N}}$, $\color{black}{L_{n-l-1}^{(l + 1/2)}}$ being a generalized Laguerre polynomial, $\color{black}{Y_{lm}}$ a spherical harmonic, constitute an orthonormal basis of the space $\color{black}{L^{2}}$ on $\color{black}{\mathbb{R}^{3}}$ with Gaussian weight $\color{black}{\exp(-r^{2})}$. These basis functions are used extensively, e.g., in biomolecular dynamic simulations. We are working on reliable algorithms to compute the Fourier coefficients of a given function with respect to the SGL basis functions in a fast way.

If you are interested in our fast SGL Fourier transforms described in our latest preprint, you can download our C++ implementation here.