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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.

UDC: 517.5

Received: 04.04.1968

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

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