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Mat. Zametki, 1969, Volume 6, Issue 4, Pages 451–462 (Mi mz6952)  

On the order of partial sums of general orthogonal series

R. S. Davtyan

Institute of Mathematics and Mechanics, Academy of Sciences of Armenian SSR

Abstract: It is shown that for convergence of every orthonormal system $\{\varphi_n(s)\}$ given on $[0,1]$, it is necessary and sufficient that, under the condition $\int_0^\infty\frac1{W^2(x)}dx<+\infty$ on tlie increasing function $W(x)$ and for $\sum_{n=1}^\infty a_n^2=+\infty$ there hold $|\sum_{k=1}^na_k\varphi_k(x)|=o(W(\sum_1^ka_k^2))$ almost everywhere on $[0,1]$.

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English version:
Mathematical Notes, 1969, 6:4, 725–732

Bibliographic databases:

UDC: 517.5
Received: 13.01.1969

Citation: R. S. Davtyan, “On the order of partial sums of general orthogonal series”, Mat. Zametki, 6:4 (1969), 451–462; Math. Notes, 6:4 (1969), 725–732

Citation in format AMSBIB
\Bibitem{Dav69}
\by R.~S.~Davtyan
\paper On the order of partial sums of general orthogonal series
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 4
\pages 451--462
\mathnet{http://mi.mathnet.ru/mz6952}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=251432}
\zmath{https://zbmath.org/?q=an:0187.02401}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 4
\pages 725--732
\crossref{https://doi.org/10.1007/BF01093810}


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