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Mat. Zametki, 1968, Volume 4, Issue 5, Pages 541–550 (Mi mz6773)  

Summation of arbitrary series by Riesz methods

L. V. Grepachevskaya

Orsk Pedagogical Insitute

Abstract: It is known (theorem of Agnew and Darevskii) that for each divergent real sequence $\{s_n\}$ and each real number $c$, there exists a $T$-method of summing $\{s_n\}$ to $c$. In this note it is shown that for each divergent sequence which is bounded above or below we can take the $T$-method in the above theorem to be a Riesz method. We also study Riesz summability of unbounded (above and below) sequences.

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English version:
Mathematical Notes, 1968, 4:5, 815–820

Bibliographic databases:

UDC: 517.5
Received: 04.04.1968

Citation: L. V. Grepachevskaya, “Summation of arbitrary series by Riesz methods”, Mat. Zametki, 4:5 (1968), 541–550; Math. Notes, 4:5 (1968), 815–820

Citation in format AMSBIB
\Bibitem{Gre68}
\by L.~V.~Grepachevskaya
\paper Summation of arbitrary series by Riesz methods
\jour Mat. Zametki
\yr 1968
\vol 4
\issue 5
\pages 541--550
\mathnet{http://mi.mathnet.ru/mz6773}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=407486}
\zmath{https://zbmath.org/?q=an:0175.34702|0172.33601}
\transl
\jour Math. Notes
\yr 1968
\vol 4
\issue 5
\pages 815--820
\crossref{https://doi.org/10.1007/BF01111316}


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