Differential properties of the operator of best approximation of complex- valued functions. II (Q1113032)

In his previous paper [Ukr. Mat. Zh. 38, No.4, 437-443 (1986; Zbl 0624.30043)] the author investigated the problem of the differentiability of the operator of the best uniform approximation of continuous functions by means of polynomials \(\sum c_ kf_ k\), where \(f_ 1,f_ 2,...,f_ n\) form a Chebyshev system, in the case when each characteristic set of the approximated function f (the set of the points x such that \(| f(x)-P(x)| =E(f)\) where E(f) is the best approximation and P(x) is the best polynomial) consists of \(2n+3\) points, the maximal possible number. This paper contains some interesting results about the same problem in the case when the number of the points in some characteristic set may be \(<2n+3\).