Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials
Let and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to satisfying . In this paper, we consider the higher-order Hermite-Fejér interpolation operator based on the zeros of and the higher order extended Hermite-Fejér interpolation op...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/542653 |
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| author | Hee Sun Jung Ryozi Sakai |
| author_facet | Hee Sun Jung Ryozi Sakai |
| author_sort | Hee Sun Jung |
| collection | DOAJ |
| description | Let and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to satisfying . In this paper, we consider the higher-order Hermite-Fejér interpolation operator based on the zeros of and the higher order extended Hermite-Fejér interpolation operator based on the zeros of . When is even, we show that Lebesgue constants of these interpolation operators are and , respectively; that is, and . In the case of the Hermite-Fejér interpolation polynomials for , we can prove the weighted uniform convergence. In addition, when is odd, we will show that these interpolations diverge for a certain continuous function on , proving that Lebesgue constants of these interpolation operators are similar or greater than log . |
| format | Article |
| id | doaj-art-c9531aaeab0e4184b9dcdf168f1b81e4 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c9531aaeab0e4184b9dcdf168f1b81e42025-08-20T02:19:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/542653542653Higher-Order Hermite-Fejér Interpolation for Stieltjes PolynomialsHee Sun Jung0Ryozi Sakai1Department of Mathematics Education, Sungkyunkwan University, Seoul 110-745, Republic of KoreaDepartment of Mathematics, Meijo University, Nagoya 468-8502, JapanLet and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to satisfying . In this paper, we consider the higher-order Hermite-Fejér interpolation operator based on the zeros of and the higher order extended Hermite-Fejér interpolation operator based on the zeros of . When is even, we show that Lebesgue constants of these interpolation operators are and , respectively; that is, and . In the case of the Hermite-Fejér interpolation polynomials for , we can prove the weighted uniform convergence. In addition, when is odd, we will show that these interpolations diverge for a certain continuous function on , proving that Lebesgue constants of these interpolation operators are similar or greater than log .http://dx.doi.org/10.1155/2013/542653 |
| spellingShingle | Hee Sun Jung Ryozi Sakai Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials Journal of Applied Mathematics |
| title | Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials |
| title_full | Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials |
| title_fullStr | Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials |
| title_full_unstemmed | Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials |
| title_short | Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials |
| title_sort | higher order hermite fejer interpolation for stieltjes polynomials |
| url | http://dx.doi.org/10.1155/2013/542653 |
| work_keys_str_mv | AT heesunjung higherorderhermitefejerinterpolationforstieltjespolynomials AT ryozisakai higherorderhermitefejerinterpolationforstieltjespolynomials |