On Local Approximation Properties of L₂-Projection on Spline-Subspaces†

Abstract

For L₂ approximations in an intervel I and a sequences by'local approximation properties' is meant whether a high regularity of the approximated function in i'will give a corresponding small error in the l₂sence for proper subintervals I" of I'. Whereas this is not so for the Fourier-sums, it holds true for projections on subspaces fulfilling certain approximability conditions which are typical for splines.