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Mikhail K. Potapov

Publications and source records attributed to Mikhail K. Potapov.

7 recordsLinked to original sources
arXiv2017

On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness

In this paper, we give a characterization of Nikol'ski\uı-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to a such a class are given. In order to prove our results, we make use of certain recent reverse Copson- and Leindler-type inequalities.

math.CA↗
arXiv2015

Some reverse $l_p$-type inequalities involving certain quasi monotone sequences

In this paper, we give some $l_p$-type inequalities about sequences satisfying certain quasi monotone type properties. As special cases, reverse $l_p$-type inequalities for non-negative decreasing sequences are obtained. The inequalities are closely related to Copson's and Leindler's inequalities, but the sign of the inequalities is reversed.

math.CA↗
arXiv2012

On Jackson's theorem for the modulus of smoothness determined by a nonsymmetric generalised shift operator

In this paper a class of asymmetrical operators of generalised translation is introduced, for each of them generalised moduli of smoothness are introduced, and Jackson's and its converse theorems are proved for those moduli. ----- V etoǐ rabote rassmatrivaetsya klass sesimmetrichnykh operatorov obobshchenogo sdviga, dlya kazhdogo iz nikh vvoditsya obobshchennye moduli gladkosti i dlya nikh dokazybaetsya teorma Dzheksona i teorema, obratnaya eǐ.

math.FA↗
arXiv2012

On a connection between a generalised modulus of smoothness of order~$r$ and the best approximation by algebraic polynomials

In this paper an asymmetrical operator of generalised translation is introduced, the generalised modulus of smoothness is defined by its means and the direct and inverse theorems in approximation theory are proved for that modulus. ----- V dannoǐ rabote vvoditsya nesimmetrichnyǐ operator obobshchennogo sdviga, s ego pomoshchyu opredelyaetsya obobshchennyǐ modul' gladkosti i dlya nego dokazyvaetsya pryamaya i obratnaya teoremy teorii priblizheniǐ.

math.FA↗