什麼樣的連續函式能由整係數多項式逼近
摘要：本文主要譯自[1]，它系統地討論了什麼樣的連續函式能由整係數多項式逼近，有以下兩種情形：
（1）區間長度大於等於4的區間上，能由整係數多項式逼近的連續函式是這些整係數多項式本身；
（2）在區間長度嚴格小於4的`區間 上，連續函式 能被整係數多項式1致逼近若且唯若 在 插值多項式為整係數多項式.
關鍵詞：逼近;整係數多項式;插值多項式;代數整數.
What Can Be Approximated by Polynomials with Integer Coefficients
Abstract: This article is mainly translated from [1] 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 錄
中文摘要 …………………………………………………………………………………………1
英文摘要 …………………………………………………………………………………………1
前言 ………………………………………………………………………………………………2
1 1些符號與專用術語…………………………………………………………………………2
2 區間長度大於等於4時整係數多項式逼近問題………………………………………………2
3 區間 與 上的整係數多項式逼近問題 ………………………………………………………4
4 區間長度小於4時的整係數多項式逼近問題…………………………………………………9
4.1代數整數及其相關概念 ………………………………………………………………………10
4.2插值多項式 ……………………………………………………………………………………10
5 結束語 …………………………………………………………………………………………15
6 參考文獻 ………………………………………………………………………………………16
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