discrete fourier analysis on fundamental domain and simplex of a (d)     lattice in d-variables

	discrete fourier analysis on fundamental domain and simplex of a (d) lattice in d-variables
	Li Huiyuan ; Xu Yuan
刊名	JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
	2010
卷号	16 期号:3 页码:383-433
关键词	Discrete Fourier analysis Lattice Fundamental domain Simplex Trigonometric Cubature Lagrange interpolation
ISSN号	1069-5869
学科主题	Mathematics ; Applied
公开日期	2011-05-23
附注	A discrete Fourier analysis on the fundamental domain Omega (d) of the d-dimensional lattice of type A (d) is studied, where Omega(2) is the regular hexagon and Omega(3) is the rhombic dodecahedron, and analogous results on d-dimensional simplex are derived by considering invariant and anti-invariant elements. Our main results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains. In particular, a trigonometric Lagrange interpolation on the simplex is shown to satisfy an explicit compact formula and the Lebesgue constant of the interpolation is shown to be in the order of (log n) (d) . The basic trigonometric functions on the simplex can be identified with Chebyshev polynomials in several variables already appeared in literature. We study common zeros of these polynomials and show that they are nodes for a family of Gaussian cubature formulas, which provides only the second known example of such formulas.
内容类型	期刊论文
源URL	[http://124.16.136.157/handle/311060/9700]
专题	软件研究所_计算机科学国家重点实验室 _期刊论文
推荐引用方式 GB/T 7714	Li Huiyuan,Xu Yuan. discrete fourier analysis on fundamental domain and simplex of a (d) lattice in d-variables[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS,2010,16(3):383-433.
APA	Li Huiyuan,&Xu Yuan.(2010).discrete fourier analysis on fundamental domain and simplex of a (d) lattice in d-variables.JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS,16(3),383-433.
MLA	Li Huiyuan,et al."discrete fourier analysis on fundamental domain and simplex of a (d) lattice in d-variables".JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 16.3(2010):383-433.