| $L^{p}_{[0,1]}$空间M"{u}ntz有理逼近的Jackson型估计 (英) |
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| 引用本文： | 虞旦盛,周颂平. $L^{p}_{[0,1]}$空间M"{u}ntz有理逼近的Jackson型估计 (英)[J]. 数学研究及应用, 2007, 27(1): 1-6 |
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| 作者姓名： | 虞旦盛 周颂平 |
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| 作者单位： | 浙江理工大学数学研究所, 浙江 杭州 310018;浙江理工大学数学研究所, 浙江 杭州 310018 |
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| 基金项目： | 国家自然科学基金(10471130) |
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| 摘 要： | 设$Lambda={lambda_{n}}_{n=1}^{infty}$为正的实数数列, 且当$nrightarrowinfty$时, 有$lambda_{n}searrow 0$.本文给出了当 $lambda_{n}leq Mn^{-frac{1}{2}},;n=1,2, cdots ,$(其中$M>0$为一正常数)时M"{u}ntz系统${x^{lambda_n}}$的有理函数在$ L_{[0,1]} ^{p}$空间的逼近速度,主要结论为$R_{n} (f, Lambda )_{L^{p}}leq C_M omega (f, n^{-frac{1}{2}})_{L^{p}},;1 leq p leq infty.$
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| 关 键 词： | M" {u}ntz有理函数 $L^p$空间 逼近速度. |
| 文章编号： | 1000-341X(2007)01-0001-06 |
| 收稿时间： | 2005-03-04 |
| 修稿时间： | 2005-03-04 |
On Jackson Estimate for M"{u}ntz Rational Approximation in $L^{p}_{[0,1]}$ Spaces |
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| YU Dan-sheng and ZHOU Song-ping. On Jackson Estimate for M"{u}ntz Rational Approximation in $L^{p}_{[0,1]}$ Spaces[J]. Journal of Mathematical Research with Applications, 2007, 27(1): 1-6 |
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| Authors: | YU Dan-sheng and ZHOU Song-ping |
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| Affiliation: | Institute of Mathematics, Zhejiang Sci-Tech University, Zhejiang 310018, China;Institute of Mathematics, Zhejiang Sci-Tech University, Zhejiang 310018, China |
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| Abstract: | Let $Lambda={lambda_{n}}_{n=1}^{infty}$ be a sequence of real numbers, and $lambda_{n}searrow 0$ as $nrightarrowinfty$. Suppose that $lambda_{n}leq Mn^{-frac{1}{2}}$ for $n=1,2, cdots$, where $M>0$ is an absolute constant. The present paper considers the M"{u}ntz rational approximation rate in $ L_{[0,1]}^{p}$ spaces and gets $R_{n} (f, Lambda )_{L^{p}}leq C_M omega (f, n^{-frac{1}{2}})_{L^{p}}$ for $1 leq p leq infty$. |
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| Keywords: | M" {u}ntz rational functions $L^p$ spaces approximation rate. |
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