Approximation on the Voronoi cells of the \(A_d\) lattice
type: Item
instance of: scholarly article
title: Approximation on the Voronoi cells of the \(A_d\) lattice
zbMATH Open document ID: 1206.41010
author: Xingping Sun
published in: Constructive Approximation
publication date: 2010-11-22T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 5818059
zbMATH Keywords: approximation
zbMATH Keywords: Dirichlet kernel
zbMATH Keywords: dual groups
zbMATH Keywords: Fejer kernel
zbMATH Keywords: Fourier series
zbMATH Keywords: interpolation
zbMATH Keywords: lattice
zbMATH Keywords: Voronoi cells
zbMATH Keywords: zonotope
describes a project that uses: kepler98
MaRDI profile type: Publication
full work available at URL: s00365-010-9116-5
OpenAlex ID: W2129121089
cites work: Q4023809
cites work: The approximation of continuous functions by positive linear operators
cites work: Q4273944
cites work: Commuting self-adjoint partial differential operators and a group theoretic problem
cites work: A proof of the Kepler conjecture
cites work: Q4839147
cites work: Q5556050
cites work: Projections of convex bodies and the Fourier transform
cites work: Q4041914
cites work: Q4090656
cites work: Discrete Fourier Analysis, Cubature, and Interpolation on a Hexagon and a Triangle
cites work: Discrete Fourier analysis on a dodecahedron and a tetrahedron
cites work: Discrete Fourier analysis on fundamental domain and simplex of \(A_{d}\) lattice in \(d\)-variables
cites work: Q3997505
cites work: Q3159056
cites work: Q4709673
cites work: Generalized Fourier transform on an arbitrary triangular domain
cites work: Q3993220
cites work: Fourier series and approximation on hexagonal and triangular domains
cites work: Q3254471
DOI: 10.1007/S00365-010-9116-5
description: scientific article; zbMATH DE number 5818059