Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group
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| Creator |
Li, H.
Sun, J. Xu, Y. |
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| Description |
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.
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| Date |
2019-02-18T12:42:41Z
2019-02-18T12:42:41Z 2012 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 41A05; 41A10 DOI: http://dx.doi.org/10.3842/SIGMA.2012.067 http://dspace.nbuv.gov.ua/handle/123456789/148448 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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