| 吴晓红,卢志康.$L_{p}$空间修正插值多项式的逼近[J].数学研究及应用,2007,27(4):883~888 |
| $L_{p}$空间修正插值多项式的逼近 |
| On Approximation by Modified Interpolation Polynomials in Spaces $L_{p}$ |
| 投稿时间：2005-07-14 修订日期：2006-07-02 |
| DOI：10.3770/j.issn:1000-341X.2007.04.036 |
| 中文关键词: 修正插值多项式 $L_{p}$空间 逼近速度. |
| 英文关键词:modified interpolation polynomials space $L_{p}[0,2\pi]$ the rate of approximation. |
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| 中文摘要: |
| 本文考虑了函数$f\in L_{p}[0,2\pi]$, $1\leq p <\infty$的特定的修正插值多项式，并给出了插值多项式对函数$f$的逼近速度的估计. 本文的估计改进了Metelichenko$^{[5]}$最近的结果. |
| 英文摘要: |
| The paper deals with certain modified interpolation polynomials for functions in space $f\in L_{p}[0,2\pi]$, $1\leq p <\infty$. An estimate of the rate of approximation to a function $f$ by these polynomials in terms of its modulus of continuity is obtained. This estimate improves essentially the result obtained by Metelichenko$^{[5]}$. |
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