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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| Дата: | 2012 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148448 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148448 |
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dspace |
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irk-123456789-1484482019-02-19T01:27:28Z Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group Li, H. Sun, J. Xu, Y. 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. 2012 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Li, H. Sun, J. Xu, Y. |
| spellingShingle |
Li, H. Sun, J. Xu, Y. Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Li, H. Sun, J. Xu, Y. |
| author_sort |
Li, H. |
| title |
Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group |
| title_short |
Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group |
| title_full |
Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group |
| title_fullStr |
Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group |
| title_full_unstemmed |
Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group |
| title_sort |
discrete fourier analysis and chebyshev polynomials with g₂ group |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148448 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT lih discretefourieranalysisandchebyshevpolynomialswithg2group AT sunj discretefourieranalysisandchebyshevpolynomialswithg2group AT xuy discretefourieranalysisandchebyshevpolynomialswithg2group |
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2023-05-20T17:30:42Z |
| last_indexed |
2023-05-20T17:30:42Z |
| _version_ |
1796153465252085760 |