线性约束逼近中统一的特征定理

Unified Characterization in Linearly Constrainted Approximation

设 f 是线性赋范空间 R 中给定的函数,K 为广义多项式集合 V^n(?)R 中满足某种线性约束条件的多项式所成的子集合。本文研究了 K 对 f 的最佳逼近的特征。我们在较一般的情况下,即对空间 R 的范数,函数 f 的性质,以及 K 所满足的线性约束条件不作任何规定的情况下,获得了一种适用范围很广的特征定理,前人已证明的多种常见的约束逼近特征定理都是本文结果的特例,特别。

Let f be a function in a given normed linear space R,K be a subset of the set of generalized polynomials V'R satisfying a certain linear constraint condition. The paper investigates the characterization of the Best approximation to f from K. When there is no limitation for the norm of R,the properties of f,and for the linear constraint condition satisfyed by K,we have a characterization theorem which has extensive applicability.Many known characterization theorems are special cases based on our results,especially,in uniform approximation without constraint,the classical characterization theorem in the form of convex hull is also a specal case of ours.