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On the bestL 1-approximations of functional classes by splines under restrictions imposed on their derivatives

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Abstract

We find the exact asymptotics (asn→∞) of the bestL 1-approximations of classesW r1 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 2π0 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→∞.

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Authors
  1. V. F. Babenko
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  2. N. V. Parfinovich
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Additional information

Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 435–444, April, 1999.

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Babenko, V.F., Parfinovich, N.V. On the bestL 1-approximations of functional classes by splines under restrictions imposed on their derivatives. Ukr Math J 51, 481–491 (1999). https://doi.org/10.1007/BF02591753

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  • DOI: https://doi.org/10.1007/BF02591753

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