Lp范数下随机连续函数空间中的Weierstrass定理

陈英伟; 王志军

doi:10.3969/j.issn.1000-1565.2018.01.002

河北大学学报(自然科学版) >

2018 , Vol. 38 >Issue 1: 7 - 11

DOI: https://doi.org/10.3969/j.issn.1000-1565.2018.01.002

L_p范数下随机连续函数空间中的Weierstrass定理

陈英伟 ,
王志军

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陈英伟(1976—), 男, 河北鸡泽人,河北经贸大学副教授, 博士,主要从事复分析与逼近论方向研究. E-mail:cyingwei@mail.ustc.edu.cn

收稿日期: 2017-08-30

网络出版日期: 2018-01-25

基金资助

河北省自然科学基金资助项目(A2015207007);河北省科技计划项目(17210310D)

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Weierstrass’s theorem in L_p spaces of random continuous function

CHEN Yingwei ,
WANG Zhijun

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College of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China

Received date: 2017-08-30

Online published: 2018-01-25

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摘要

通过概率方法对随机连续函数的多项式逼近性质进行了研究. 借助随机Bernstein算子给出了L_p范数下随机系数多项式逼近的定性估计, 进而推广了Weierstrass定理.

关键词： 随机连续函数; Weierstrass定理; 随机Bernstein算子; 随机系数多项式

本文引用格式

陈英伟 , 王志军 . L_p范数下随机连续函数空间中的Weierstrass定理[J]. 河北大学学报(自然科学版), 2018 , 38(1) : 7 -11 . DOI: 10.3969/j.issn.1000-1565.2018.01.002

Abstract

The purpose of this article is to investigate polynomial approximation properties of random continuous function by the probability method. We obtained the qualitative estimation by random Bernstein’s operator with L_p norm and extended Weierstrass's theorem to random continuous function spaces further.

Key words： random continuous function; Weierstrass's theorem; random Bernstein's operator; random coefficient polynomial

参考文献

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