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Mat. Zametki, 2019, Volume 105, Issue 4, Pages 545–552 (Mi mz12069)  

A Sobolev Orthogonal System of Functions Generated by a Walsh System

M. G. Magomed-Kasumovab

a Vladikavkaz Scientific Centre of the Russian Academy of Sciences
b Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala

Abstract: Properties of functions from the Sobolev orthogonal system $\mathfrak W_r$ generated by the Walsh system are studied. In particular, recurrence relations for functions from $\mathfrak W_1$ are obtained. The uniform convergence of Fourier series in the system $\mathfrak W_r$ to functions $f$ from the Sobolev spaces $W^r_{L^p}$, $p\ge 1$, $r=1,2,…$ is proved.

Keywords: Sobolev orthogonality, Walsh system, uniform convergence, recurrence relation.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-31-00477
This work was supported by the Russian Foundation for Basic Research under grant 18-31-00477 mol_a.


DOI: https://doi.org/10.4213/mzm12069

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UDC: 517.521
Received: 23.05.2018
Revised: 10.07.2018

Citation: M. G. Magomed-Kasumov, “A Sobolev Orthogonal System of Functions Generated by a Walsh System”, Mat. Zametki, 105:4 (2019), 545–552

Citation in format AMSBIB
\Bibitem{Mag19}
\by M.~G.~Magomed-Kasumov
\paper A Sobolev Orthogonal System of Functions Generated by a Walsh System
\jour Mat. Zametki
\yr 2019
\vol 105
\issue 4
\pages 545--552
\mathnet{http://mi.mathnet.ru/mz12069}
\crossref{https://doi.org/10.4213/mzm12069}
\elib{http://elibrary.ru/item.asp?id=37180560}


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