Institutional Repository
| discrete fourier analysis and chebyshev polynomials with g(2) group | |
| Li Huiyuan; Sun Jiachang; Xu Yuan | |
| 2012 | |
| Source | SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
 |
| ISSN | 1815-0659 |
| Volume | 8Pages:- |
| English Abstract | The discrete Fourier analysis on the 30 degrees-60 degrees-90 degrees triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group G(2), which leads to the definition of four families generalized Chebyshev polynomials. The study of these polynomials leads to a Sturm-Liouville eigenvalue problem that contains two parameters, whose solutions are analogues of the Jacobi polynomials. Under a concept of m-degree and by introducing a new ordering among monomials, these polynomials are shown to share properties of the ordinary orthogonal polynomials. In particular, their common zeros generate cubature rules of Gauss type.; The discrete Fourier analysis on the 30 degrees-60 degrees-90 degrees triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group G(2), which leads to the definition of four families generalized Chebyshev polynomials. The study of these polynomials leads to a Sturm-Liouville eigenvalue problem that contains two parameters, whose solutions are analogues of the Jacobi polynomials. Under a concept of m-degree and by introducing a new ordering among monomials, these polynomials are shown to share properties of the ordinary orthogonal polynomials. In particular, their common zeros generate cubature rules of Gauss type. |
| Indexed Type | SCI |
| Keyword | Discrete Fourier Series Trigonometric Group g(2) Pde Orthogonal Polynomials |
| Department | Li Huiyuan; Sun Jiachang Chinese Acad Sci Inst Software Beijing 100190 Peoples R China. Xu Yuan Univ Oregon Dept Math Eugene OR 97403 USA. |
| Subject | Physics |
| Sponsorship | NSFC 10971212, 91130014, 60970089; NSF DMS-110 6113; Simons Foundation 209057 |
| Language | 英语 |
| WOS ID | WOS:000309390300001 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/15097 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Li Huiyuan,Sun Jiachang,Xu Yuan. discrete fourier analysis and chebyshev polynomials with g(2) group[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS,2012,8:-. |
| APA | Li Huiyuan,Sun Jiachang,&Xu Yuan.(2012).discrete fourier analysis and chebyshev polynomials with g(2) group.SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS,8,-. |
| MLA | Li Huiyuan,et al."discrete fourier analysis and chebyshev polynomials with g(2) group".SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 8(2012):-. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment