Abstract: | We find the exact asymptotics (asn→∞) of the bestL 1-approximations of classesW 1 r of periodic functions by spliness∈S 2n, r∼-1 (S 2n, r∼-1 is a set of 2π-periodic polynomial splines of orderr−1, defect one, and with nodes at the pointskπ/n,k∈ℤ) such that V 0 2π s( r-1)≤1+ɛ n , where {ɛ n } n=1 ∞ is a decreasing sequence of positive numbers such that ɛ n n 2→∞ and ɛ n →0 asn→∞. Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 435–444, April, 1999. |