For citation:
Volosivets S. S., Likhacheva T. V. Several Questions of Approximation by Polynomials with Respect to Multiplicative Systems in Weighted Lp Spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 3, pp. 251-257. DOI: 10.18500/1816-9791-2015-15-3-251-258, EDN: UKIVDH
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
11.09.2015
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Russian
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UDC:
517.518
EDN:
UKIVDH
Several Questions of Approximation by Polynomials with Respect to Multiplicative Systems in Weighted Lp Spaces
Autors:
Volosivets Sergei Sergeevich, Saratov State University
Likhacheva Tatyana Vladimirovna, Saratov State University
Abstract:
In this paper we study approximation by Vilenkin polynomials in weighted Lp spaces. We prove the Butzer – Scherer type result on equivalence between the rate of best approximation of a function f and the growth of generalized derivatives and approximating properties of the best approximation polynomial tn(f). Some applications to the approximation by linear means of the Fourier – Vilenkin series are given.
References:
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Received:
22.04.2015
Accepted:
27.08.2015
Published:
30.09.2015
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