On the best approximation of vector valued functions by polynomials with coefficients in vector spaces


In this paper, we prove some basic results concerning the best approximation of vector-valued functions by algebraic and trigonometric polynomials with coefficients in normed spaces, called generalized polynomials. Thus we obtain direct and inverse theorems for the best approximation by generalized polynomials and results concerning the existence (and uniqueness) of best approximation generalized polynomials. © 2006 Springer-Verlag.

Publication Title

Annali di Matematica Pura ed Applicata