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- W2043114694 abstract "The problem whether a real sequence $({s_i})$ has a dilution which is $(C,1)$ summable to a number $s$ is transformed by means of two sequences measuring the oscillation of $({s_i})$ about $s$. (If it does not oscillate, the condition, known, is that $s$ is a limit point of $({s_i})$.) For the $j$th consecutive block of ${s_i}$ on one side of $s,{alpha _j}$ is the minimum of their distances from $s,{beta _j}$ the sum of distances. Then there must exist positive numbers ${p_j}$ such that ${beta _j} + {p_j}{alpha _j} = o({p_1} + cdots + {p_{j - 1}})$. The necessary condition and the sufficient condition coincide for very smooth sequences at ${alpha _i}log {beta _i} = o(i)$." @default.
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- W2043114694 date "1974-03-01" @default.
- W2043114694 modified "2023-10-18" @default.
- W2043114694 title "On dilution and Cesàro summation" @default.
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- W2043114694 doi "https://doi.org/10.1090/s0002-9939-1974-0350250-2" @default.
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