Constructive Approximation

The book describes function spaces used in approximation, the needed functional analytic tools. It develops basic properties of polynomials, splines, linear operators that are used for approximation (and interpolation). The book takes the reader up to and into the recent great advances of Approximation Theory and emphasizes good proofs, logical selection of material, avoidance of superfluous details.

Special cases of Haar systems on [a, b] are the Polya systems. Their definition is
based on the following remarks: 1. If V = {vo,...,Vk-\} is a Haar system on \a,b] and
w € C[a, b] is strictly positive, then W := {wv0 wvk-i} is also a Haar system on [a, ...