On the Exact Asymptotics of the Best Relative Approximations of Classes of Periodic Functions by Splines - Parfinovych, N. V. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
We obtain the exact asymptotics (as n → ∞) of the best L 1-approximations of classes \(W_1^r\) of periodic functions by splines s ∈ S 2n, r − 1 and s ∈ S 2n, r + k − 1 (S 2n, r is the set of 2π-periodic polynomial splines of order r and defect 1 with nodes at the points kπ/n, k ∈ Z) under certain restrictions on their derivatives.