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Matematicheskie Zametki, 1968, Volume 3, Issue 3, Pages 345–356 (Mi mzm6687)  
Approximation by linear methods of summation of orthogonal series

È. A. Storozhenko

I. I. Mechnikov Odessa State University
Full-text PDF (581 kB) English version article
Abstract: We give an estimate of the rapidity of convergence of certain linear means of the orthogonal series $\sum_{k=0}^\infty c_k\varphi_k(x)$ to the function $f(x)\in L_2(a,b)$ defined by this series according to the Riesz-Fisher theorem for almost all $x\in(a,b)$. The results obtained are, in a certain sense, final.
Received: 20.06.1967
English version:
Mathematical Notes, 1968, Volume 3, Issue 3, Pages 218–224
DOI: https://doi.org/10.1007/BF01387338
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: È. A. Storozhenko, “Approximation by linear methods of summation of orthogonal series”, Mat. Zametki, 3:3 (1968), 345–356; Math. Notes, 3:3 (1968), 218–224
Citation in format AMSBIB
\Bibitem{Sto68}
\by \`E.~A.~Storozhenko
\paper Approximation by linear methods of summation of orthogonal series
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 3
\pages 345--356
\mathnet{http://mi.mathnet.ru/mzm6687}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=227676}
\zmath{https://zbmath.org/?q=an:0197.05001}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 3
\pages 218--224
\crossref{https://doi.org/10.1007/BF01387338}
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