Upper bounds for the best one-sided approximation by splines of the classes WrL1 |
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Authors: | V. G. Doronin A. A. Ligun |
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Affiliation: | (1) Dnepropetrovsk State University, USSR;(2) Dneprodzershinsk Industrial Institute, USSR |
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Abstract: | In the present note we will investigate the problem of the one-sided approximation of functions by n-dimensional subspaces. In particular, we will find the exact value of the best one-sided approximation of the class WrL1 (r=1, 2, ...) of all periodic functions f(x) of period 2 for which f(r–1)(x) (f(0)(x)=f(x)) is absolutely continuous and f(r)L11 by periodic spline functions S2n ( = 0, 1, ..., n=1, 2, ...) of period 2, order ,and deficiency 1.Translated from Matematicheskie Zametki, Vol. 19, No. 1, pp. 11–17, January, 1976. |
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