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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148448 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862722077773004800 |
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| author | Li, H. Sun, J. Xu, Y. |
| author_facet | Li, H. Sun, J. Xu, Y. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-07T18:33:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148448 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:33:49Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Li, H. Sun, J. Xu, Y. 2019-02-18T12:42:41Z 2019-02-18T12:42:41Z 2012 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 https://nasplib.isofts.kiev.ua/handle/123456789/148448 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. 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). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group Article published earlier |
| spellingShingle | Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group Li, H. Sun, J. Xu, Y. |
| title | 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_short | Discrete Fourier Analysis and Chebyshev Polynomials with G₂ Group |
| title_sort | discrete fourier analysis and chebyshev polynomials with g₂ group |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148448 |
| work_keys_str_mv | AT lih discretefourieranalysisandchebyshevpolynomialswithg2group AT sunj discretefourieranalysisandchebyshevpolynomialswithg2group AT xuy discretefourieranalysisandchebyshevpolynomialswithg2group |