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Subject: Physics
Title:
discrete fourier analysis and chebyshev polynomials with g(2) group
Author: Li Huiyuan ; Sun Jiachang ; Xu Yuan
Keyword: discrete Fourier series ; trigonometric ; group G(2) ; PDE ; orthogonal polynomials
Source: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
Issued Date: 2012
Volume: 8, Pages:-
Indexed Type: SCI
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.
Sponsorship: NSFC 10971212, 91130014, 60970089; NSF DMS-110 6113; Simons Foundation 209057
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.
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.
Language: 英语
WOS ID: WOS:000309390300001
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/15097
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Li Huiyuan,Sun Jiachang,Xu Yuan. discrete fourier analysis and chebyshev polynomials with g(2) group[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS,2012-01-01,8:-.
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