| ON THE GENERALIZATIONS OF KALANDIA＇S LEMMA |
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| 作者姓名： | Yafang Gong |
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| 作者单位： | [1]Wuhan University, China [2]School of Mathematics and StatisticsWuhan University, Wuhan, 430072 P. R. China |
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| 基金项目： | Supported by National Natural Science Foundation of China （No. 10471107） and SF of Wuhan University （No. 20127004）. Acknowledgements The author appreciates professors Jianke Lu and Jinyuan Du for their long-term helps. Many thanks to Profssor Jinyuan Du who provided me A. I. Kalandia＇s paper.. |
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| 摘 要： | Based on Bernstein＇s Theorem, Kalandia＇s Lemma describes the error estimate and the smoothness of the remainder under the second part of Hoelder norm when a HSlder function is approximated by its best polynomial approximation. In this paper, Kalandia＇s Lemma is generalized to the cases that the best polynomial is replaced by one of its four kinds of Chebyshev polynomial expansions, the error estimates of the remainder are given out under Hoeder norm or the weighted HSlder norms.
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| 关 键 词： | 余数 多项式 正交级数 函数 |
| 收稿时间： | 15 March 2006 |
| 修稿时间： | 2006-03-15 |
On the generalizations of Kalandia’s Lemma |
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| Yafang Gong.On the generalizations of Kalandia’s Lemma[J].Analysis in Theory and Applications,2006,22(4):329-338. |
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| Authors: | Yafang Gong |
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| Institution: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China |
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| Abstract: | Based on Bernstein’s Theorem, Kalandia’s Lemma describes the error estimate and the smoothness of the remainder under the second part of Hölder norm when a Hölder function is approximated by its best polynomial approximation. In this paper, Kalandia’s Lemma is generalized to the cases that the best polynomial is replaced by one of its four kinds of Chebyshev polynomial expansions, the error estimates of the remainder are given out under Hölder norm or the weighted Hölder norms. |
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| Keywords: | Chebyshev polynomials Chebyshev norm weighted Hoeder norm |
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