discrete fourier analysis on fundamental domain and simplex of a (d) lattice in d-variables
文献类型：期刊论文
| 作者 | Li Huiyuan ; Xu Yuan |
| 刊名 | JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
 |
| 出版日期 | 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. |
| 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. |
入库方式： OAI收割
来源：软件研究所
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。