| Shepard-Lagrange算子的逼近 |
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| 引用本文： | 虞旦盛.Shepard-Lagrange算子的逼近[J].数学学报,2010,53(1):97-108. |
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| 作者姓名： | 虞旦盛 |
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| 作者单位： | 杭州师范大学数学系; |
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| 基金项目： | 杭州师范大学科研启动项目 |
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| 摘 要： | 本文建立了Shepard-Lagrange算子逼近的正逆定理,证明了可以利用高阶光滑模来刻画Shepard-Lagrange算子的逼近性质.从而说明了Shepard-Lagrange算子比一般的Shepard算子具有更好的逼近性质.进一步,所用光滑模的阶梯函数非常广泛,这是多项式逼近所不具有的.
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| 关 键 词： | Shepard-Lagrange算子 正逆定理 点态和整体估计 |
| 收稿时间： | 2008-12-01 |
| 修稿时间： | 2009-04-09 |
On Approximation by Shepard--Lagrange Operators |
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| Dan Sheng YU.On Approximation by Shepard--Lagrange Operators[J].Acta Mathematica Sinica,2010,53(1):97-108. |
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| Authors: | Dan Sheng YU |
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| Institution: | Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, P. R. China |
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| Abstract: | We establish direct and inverse results of the approximation by the Shepard-Lagrange operators.It was shown that we can use higher modulus of smoothness to characteristic the approximation of the Shepard-Lagrange operators,and thus the Shepard-Lagrange operators have better approximation properties than the usual Shepard operators.Furthermore,the higher modulus of smoothness involves a very general class of step functions,which can not be obtained by polynomial approximation. |
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| Keywords: | Shepard-Lagrange operators direct and inverse theorems pointwise and global estimates |
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