关于系数有界限的多项式的最佳逼近

The Best Approximation of Polynomials with Bound Coeffricents

设X是区间[a,b](a·b≥0)上的紧集,f是X上的一个连续函数,K={p=∑_-0αf x^f:α_j≤α_j≤β_j,j=0,1…,n}为系数有界限的多项式之集合。本文给出了K对f的最佳一致逼近的一个交错点型的特征定理。

Let X be a compact subset of an interval [a, b] (a·b≥0), f a continuous function definid on X. By K={p=∑_j^n-0 a_jx^j:a_j≤a;≤β_j, j=0, 1, …,n} we denote the set of algebraic polynomials having bounded coefficient. The paper gives a characterization, theorem in form of alternation for the polynamial of best approximation to f from K.