Abstract:
A class of linear methods is distinguished which possesses the property: each method sums almost everywhere any orthogonal series in $L_2$ if and only if a subsequence of partial sums whose indices satisfy a certain condition and do not depend on the series converges almost everywhere. Questions are considered on the exact Weyl multiplier and strong summability.
\Bibitem{Bol68}
\by V.~A.~Bolgov
\paper The summation of orthogonal series by linear methods
\jour Mat. Zametki
\yr 1968
\vol 4
\issue 6
\pages 697--705
\mathnet{http://mi.mathnet.ru/mzm6790}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=243267}
\zmath{https://zbmath.org/?q=an:0174.36101}
\transl
\jour Math. Notes
\yr 1968
\vol 4
\issue 6
\pages 907--912
\crossref{https://doi.org/10.1007/BF01110827}
Linking options:
https://www.mathnet.ru/eng/mzm6790
https://www.mathnet.ru/eng/mzm/v4/i6/p697
This publication is cited in the following 3 articles:
H. Schwinn, “Strong summability and convergence of subsequences of orthogonal series”, Acta Math Hung, 50:1-2 (1987), 21
O. A. Ziza, “On Weyl factors for the summability almost everywhere of orthogonal series by $(\varphi,\lambda)$-methods”, Russian Math. Surveys, 38:6 (1983), 139–141
V. A. Bolgov, A. V. Efimov, “On the rate of summability of orthogonal series”, Math. USSR-Izv., 5:6 (1971), 1399–1417