%0 Journal Article
%T Discrete Fourier Analysis and Chebyshev Polynomials with G2 Group
%A Huiyuan Li
%A Jiachang Sun
%A Yuan Xu
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2012
%I National Academy of Science of Ukraine
%X The discrete Fourier analysis on the 30กใ-60กใ-90กใ triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group G2, 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.
%K discrete Fourier series
%K trigonometric
%K group G2
%K PDE
%K orthogonal polynomials
%U http://dx.doi.org/10.3842/SIGMA.2012.067