RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 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 $[0,1]$.

Full text: PDF file (622 kB)

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

Bibliographic databases:

UDC: 517.5

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}