Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.518
DOI: 
10.18500/1816-9791-2015-15-3-251-258
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.

Key words: 
Vilenkin system
best approximation
generalized derivative
Zygmund – Riesz means
References: 
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Received: 
22.04.2015
Accepted: 
27.08.2015
Published: 
30.09.2015
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