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Эта публикация цитируется в 10 научных статьях (всего в 10 статьях)
Discrete Fourier analysis and Chebyshev polynomials with $G_2$ group
Huiyuan Lia, Jiachang Suna, Yuan Xub a Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
b Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222, USA
Аннотация:
The discrete Fourier analysis on the $30^{\circ}$–$60^{\circ}$–$90^{\circ}$ 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.
Ключевые слова:
discrete Fourier series; trigonometric; group $G_2$; PDE; orthogonal polynomials.
Поступила: 4 мая 2012 г.; в окончательном варианте 6 сентября 2012 г.; опубликована 3 октября 2012 г.
Образец цитирования:
Huiyuan Li, Jiachang Sun, Yuan Xu, “Discrete Fourier analysis and Chebyshev polynomials with $G_2$ group”, SIGMA, 8 (2012), 067, 29 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma744 https://www.mathnet.ru/rus/sigma/v8/p67
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