具限制系数广义多项式集的最佳同时逼近特征

在复赋范线性空间X中考察了具限制系数的广义多项式集G对全有界序列(xv)的加权同时逼近问题.用只含有限个点的序列逼近全有界序列(xv)，然后把只含有限个点的序列的逼近问题转化为复值连续函数空间中的Chebyshev逼近问题，在X一致光滑及inf v∈N d(xv,G)>0的条件下，给出了G对(xv)逼近的特征定理.

Characterizations of Best Simultaneous Approximation from Sets of Generalized Polynomials with Restricted Coefficients

This paper investigates the problem of the best weighted simultaneous approximation to totally bounded sequences ( xv ) from a set G of generalized polynomials with restricted coefficients in complex normed linear spaces X. By approximating a totally bounded sequence ( xv ) via sequences consisting of finite many points in X, and then by transforming the problem of the best simultaneous approximation to a sequence consisting of finite many points in X into that of the best Chebyshev approximation in a complex-valued continuous functions space, the author gives characteristic results of the best simultaneous approximation to ( xv ) from G under the assumptions that X is uniformly smooth and infv∈N d( xv, G) ＞ 0.