Vector Approximation

Abstract

Vector approximation problems are abstract approximation problems where a vectorial norm is used instead of a usual (real-valued) norm. Many important results known from approximation theory can be extended to this vector-valued case. After a short introduction we examine the relationship between vector approximation and simultaneous approximation, and we present the so-called generalized Kolmogorov condition. Moreover, we consider nonlinear and linear Chebyshev vector approximation problems and we formulate a generalized alternation theorem for these problems.