The Convergence of Hermite Interpolation Operators on the Real Line
Received:October 12, 2005  Revised:December 01, 2005
Key Words: convergence   Hermite interpolation   real line.  
Fund Project:Open Funds of State Key Laboratory of Oil and Gas Reservoir and Exploitation, Southwest Petroleum University (No. PCN0613); the Natural Foundation of Education of Zhejiang Province (No. Kyg091206029).
Author NameAffiliation
ZHAO Yi Institute of Mathematics, Hangzhou Dianzi University, Zhejiang 310018, China 
LI Jiang-bo Department of Mathemataics, Lishui Teacher's College, Zhejiang 323000, China 
ZHOU Song-ping Institute of Mathematics, Zhejiang Sci-Tech University, Zhejiang 310018, China 
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      The present paper investigates the convergence of Hermite interpolation operators on the real line. The main result is: Given $0<\delta_{0}<1/2$, $0<\epsilon_{0}<1$. Let $f\in C_{(- \infty,\infty)}$ satisfy $|y_{k}| = O(e^{(1/2-\delta_{0})x_{k}^{2}})$ and $|f(x)| = O(e^{(1-\epsilon_{0})x^{2}})$. Then for any given point $x\in \R$, we have $\lim_{n\to\infty}H_{n}(f,x)=f(x)$.
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