复域中扰动Fejér点上Hermite--Fejér插值逼近的稳定性

涂天亮, 邓继恩

数学学报 ›› 2010, Vol. 53 ›› Issue (2) : 393-408.

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数学学报 ›› 2010, Vol. 53 ›› Issue (2) : 393-408. DOI: 10.12386/A2010sxxb0046
论文

复域中扰动Fejér点上Hermite--Fejér插值逼近的稳定性

    涂天亮, 邓继恩
作者信息 +

Stability of Approximation by Hermite--Fejé Interpolation at Disturbed Fej´er Point in the Complex Domain

    Tian Liang TU, Ji En DENG
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摘要

该文在Jordan区域上研究扰动Fejér点上Hermite--Fejér插值对的逼近阶与收敛性, 完全解决了美国数学会 1991年Transactions of the AMS中Chui和Shen提出的问题,并将其边界条件J2改进为.  

Abstract

For the convergence and order of approximation to by Hermite--Fejér interpolation at disturbed Fejér points on Γ, the open problem posed by Chui & Shen in Transactions of the AMS 1991 is solved completely. In the meantime, the boundary condition J2 is improved by in this paper.  

关键词

扰动Fejér点 / Hermite--Fejér插值 / 稳定的收敛性和逼近阶

Key words

disturbed Fejér points / Hermite--Fejér interpolation / stable convergence and order of approximation

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涂天亮, 邓继恩. 复域中扰动Fejér点上Hermite--Fejér插值逼近的稳定性. 数学学报, 2010, 53(2): 393-408 https://doi.org/10.12386/A2010sxxb0046
Tian Liang TU, Ji En DENG. Stability of Approximation by Hermite--Fejé Interpolation at Disturbed Fej´er Point in the Complex Domain. Acta Mathematica Sinica, Chinese Series, 2010, 53(2): 393-408 https://doi.org/10.12386/A2010sxxb0046

参考文献



[1] Chui C. K., Shen X. C., On Hermite--Fejér interpolation in a Jordan domain, Trans. Amer. Math. Soc., 1991, 323(1): 93--109.



[2] Markushevech A. I., Theory of Analytic Functions (in Russian), Moscow: GIT-TL, 1950.



[3] Goncharov B. L., Theory of Interpolation and Approximation to Functions, Chapter 1. Moskwa: GIT-TL, 1954.



[4] Shen X. C., Shuai B. P., Order of approximation by Lagronge interpolation polynomiais at nearly roots of unity, J. of Math., (PRC), 1991, 11(3): 287--297 (in Chinese).



[5] TU T. L., Jackson type theorems on complex curve, Sci. in China Ser. A, 2009, 52(3): 493--506.



[6] Pólya G., Szegö G., Problems and Theorems in Analysis (in Russian), Moscow: GIT-TL, 1956, I p.60; p.233.



[7] TU T. L., The Simultaneous approximation order by Hermite interpolation in a smooth domain, Acta Mathematica Sinica, English Series, 2002, 18(4): 631--646.



[8] Zygmund A., Trigonometric Series, Vols I II, Cambridge: Cambridge Univ. Press, 1968.



[9] Dzyadyk V. K., Introduction of Uniform Approximation to Functions by Polynomials (in Russian), Moscow: Nauk, 1977.

基金

国家自然科学基金项目(10671041);安徽省教育厅一般项目(KJ2008B244)

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