discrete fourier analysis and chebyshev polynomials with g(2) group

ISCAS OpenIR

	discrete fourier analysis and chebyshev polynomials with g(2) group
	Li Huiyuan; Sun Jiachang; Xu Yuan
	2012
发表期刊	SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
ISSN	1815-0659
卷号	8 页码:-
摘要	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.
收录类别	SCI
关键词	Discrete Fourier Series Trigonometric Group g(2) Pde Orthogonal Polynomials
部门归属	Li Huiyuan; Sun Jiachang Chinese Acad Sci Inst Software Beijing 100190 Peoples R China. Xu Yuan Univ Oregon Dept Math Eugene OR 97403 USA.
学科领域	Physics
资助者	NSFC 10971212, 91130014, 60970089; NSF DMS-110 6113; Simons Foundation 209057
语种	英语
WOS记录号	WOS:000309390300001
引用统计	被引频次：12[WOS] [WOS记录] [WOS相关记录]
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/15097
专题	中国科学院软件研究所
推荐引用方式 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):-.