Discretization of compact semisimple Lie groups
Jiří Hrivnák, J. Patera, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov · AIP conference proceedings · 2008
An efficient construction of lattice points FM of any density and any admissible symmetry is described in a finite region F⊃FM of a real n‐dimensional Euclidean space. The shape of F and the lattice symmetry of FM is determined by a compact semisimple Lie group of rank n underlying the construction. The density of FM is fixed by our choice of a positive integer M, where 1⩽M<∞. The Lie group allows one to introduce systems of special functions discretely orthogonal on FM together with the possibility of expanding digital data on FM into finite series of such special functions.