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Daghestan Electronic Mathematical Reports, 2019, Issue 12, Pages 55–61 (Mi demr77)  

On uniform convergence of Fourier-Sobolev series

T. N. Shakh-Emirov

Department of Mathematics and Informatics, DFRC, Makhachkala

Abstract: Let $\{\varphi_{k}\}_{k=0}^\infty$ be a system of functions defined on $ [a, b] $ and orthonormal in $ L ^ 2_ \rho = L ^ 2_\rho ( a, b) $ with respect to the usual inner product. For a given positive integer $ r $, by $\{\varphi_{r,k}\}_{k=0}^\infty$ we denote the system of functions orthonormal with respect to the Sobolev-type inner product and generated by the system $\{\varphi_{k}\}_{k=0}^\infty$. In this paper, we study the question of the uniform convergence of the Fourier series by the system of functions $\{\varphi_{r,k}\}_{k=0}^\infty$ to the functions $f\in W^r_{L^p_\rho}$ in the case when the original system $\{\varphi_{k}\}_{k=0}^\infty$ forms a basis in the space $L^p_\rho=L^p_\rho(a,b)$ ($1\le p$, $p\neq2$).

Keywords: Fourier series; Sobolev-type inner product; Sobolev space; Sobolev-orthonormal functions

DOI: https://doi.org/10.31029/demr.10.7

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UDC: 517.538
Received: 20.08.2019
Revised: 26.09.2019
Accepted:27.09.2019

Citation: T. N. Shakh-Emirov, “On uniform convergence of Fourier-Sobolev series”, Daghestan Electronic Mathematical Reports, 2019, no. 12, 55–61

Citation in format AMSBIB
\Bibitem{Sha19}
\by T.~N.~Shakh-Emirov
\paper On uniform convergence of Fourier-Sobolev series
\jour Daghestan Electronic Mathematical Reports
\yr 2019
\issue 12
\pages 55--61
\mathnet{http://mi.mathnet.ru/demr77}
\crossref{https://doi.org/10.31029/demr.10.7}


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