复赋范空间中复RS集的最佳同时逼近

Best simultaneous approximation from complex RS-sets in complex normed spaces

研究了复赋范空间中具限制系数的广义多项式集G对无穷序列的最佳同时逼近问题,得到了特征定理;当G是复RS集时还得到了惟一性定理.

This paper is concerned with the problem of the best simultaneous approximation from generalized polynomials with restricted coefficients to an infinite sequence in complex normed linear spaces. The characterizations of the best approximation from generalized polynomials with restricted coefficients are proved and the uniqueness of the best approximation from a complex RS-set is given.