Approximation on the Voronoi cells of the \(A_d\) lattice
The paper deals with the study of several approximation problems on the Voronoi cells of the \(A_d\) lattice. The study depends on discretization of the Voronoi cells induced by a zonotopal algebra and finite quotient groups. The latter provides a natural tool for doing discrete Fourier analysis on the Voronoi cells. The intersections between the groups and their dual groups yield interpolation and quadrature formulas on the Voronoi cells. The zonotope structure allows one to investigate the approximation property of several types of kernels on the Voronoi cells. The Fejer type kernel can also be realized as a summability method. As comparison to the classic \((C,1)\) summability which assigns equal weight to the partial sums of a Fourier series, the Fejer type summability method on the Voronoi cells assigns equal weights to about half of the partial sums and algebraically decaying weights to the rest.
scientific article; zbMATH DE number 5818059
scientific article