Inequalities for polynomial splines

Abstract

We establish exact estimates for the variation on a period of the derivative s ^(r)(t) of a periodic polynomial spline s(t) of degree r and defect 1 with respect to a fixed partition of [0, 2π) under the condition that \(\left\| {s^{(r)} } \right\|_X = 1\) , where X=C or L ₁