Abstract
We solve a problem of S. B. Stechkin concerning the best approximation in the metric of C to the operator of k-th order differentiation on certain classes of differentiable functions defined on the half-line, by linear operators whose norms from L2 into C are bounded. We consider the analogous problem for linear differential operators with constant coefficients. The bibliography contains 10 items.
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Translated from Matematicheskie Zametki, Vol. 6, No. 5, pp. 573–582, November, 1969.
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Gabushin, V.N. On the best approximation of the differentiation operator on the half-line. Mathematical Notes of the Academy of Sciences of the USSR 6, 804–810 (1969). https://doi.org/10.1007/BF01101408
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DOI: https://doi.org/10.1007/BF01101408