Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148448 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |