Abstract
In this paper the coincidence of two classes of functions is proved. One of them is determined by the power order of best polynomial approximation. To define the other class, first a new nonsymmetric generalized shift operator is introduced, and next, with its help we introduce a generalized modulus of continuity whose power order determines the second class of functions.
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Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 242–257, August, 1999.
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Potapov, M.K. Coincidence of classes of functions defined by the generalized shift operator or by the order of best polynomial approximation. Math Notes 66, 190–202 (1999). https://doi.org/10.1007/BF02674877
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DOI: https://doi.org/10.1007/BF02674877