Approximation of analytic functions by linear methods of summation of Taylor series

Mykola A. Veremii, Mykola V. Haevskyi, Petro V. Zaderei


In this paper we find estimates for the deviation of polynomials generated by general linear methods of summation of Taylor series on the spaces of analytic functions $ H^{\psi}_\infty $ (Kolmogorov–Nikolsky problem). These classes, generated by the sequence $ \{\psi (k)\}^\infty_{k = 0}, \psi (k) = \psi_1 (k) + i \psi_2 (k) $, are analogues of classes of differentiable functions, which were introduced by A. I. Stepanets. In the sequence $ \{\psi_i (k)\}, i = 1,2 $, the Boas–Telyakovskii conditions are superimposed.

The deviation of polynomials is considered in a uniform metric.


Taylor series; Analytic functions; Linear summation methods; Spaces of functions; Matrix of complex numbers


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