Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group
Інший ID:
2010 Mathematics Subject Classification: 41A05; 41A10
DOI: http://dx.doi.org/10.3842/SIGMA.2012.067
DOI: http://dx.doi.org/10.3842/SIGMA.2012.067
Посилання:
Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group / H. Li, J. Sun, Y. Xu // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 19 назв. — англ.
Підтримка:
The work of the first author was partially supported by NSFC Grants 10971212 and 91130014.The work of the second author was partially supported by NSFC Grant 60970089. The work of the third author was supported in part by NSF Grant DMS-110 6113 and a grant from the Simons Foundation (# 209057 to Yuan Xu).
Дата:
2012
Переглядів:
556
Завантажень:
269
Анотація:
The discrete Fourier analysis on the 30°-60°-90° 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.
