什么样的连续函数能由整系数多项式逼近

什么样的连续函数能由整系数多项式逼近

摘要：本文主要译自[1]，它系统地讨论了什么样的连续函数能由整系数多项式逼近，有以下两种情形：
（1）区间长度大于等于4的区间上，能由整系数多项式逼近的连续函数是这些整系数多项式本身；
（2）在区间长度严格小于4的区间 上，连续函数 能被整系数多项式1致逼近当且仅当 在 插值多项式为整系数多项式.

关键词：逼近;整系数多项式;插值多项式;代数整数.

What Can Be Approximated by Polynomials with Integer Coefficients

Abstract: This article is mainly translated from [1].What can be approximated by polynomials with integer coefficients is given in the following two aspects:
(1)If the interval has length four or more than the only functions that are approximable on the interval by polynomials with integer coefficients are these polynomials themselves.
 (2) If   is a continuous function on an interval I of length strictly less then 4,then  is approximable on the interval by polynomials with integer coefficients if and only if its interpolating polynomial on   has integer coefficients.

Keywords: approximation; polynomial with integer coefficients; interpolating polynomial; algebraic integer.

目  录

中文摘要  …………………………………………………………………………………………1
英文摘要  …………………………………………………………………………………………1
前言　………………………………………………………………………………………………2
1  1些符号与专用术语…………………………………………………………………………2

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