Exact values of best approximations for classes of periodic functions by splines of deficiency 2
Let \(X\) be the class of periodic functions whose \(r\)th derivative is a a given rearrangement-invariant set of a class of periodic functions having an \(r\)th derivative whose modulus of continuity is bounded by a given convex function, and let \(m \geq r+1\). For either of these function spaces, the authors provide exact values for the best \(L_1\)-approximations using polynomial splines of order \(m\) and deficiency 2 with equispaced nodes. In addition, these spline spaces are shown to be extremal for the Kolmogorov widths in the function class \(X\).
scientific article; zbMATH DE number 5628181