A Characterization of Cesaro Convergence

2020/12/26 by Leonetti, Paolo
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.13733

Abstract

We show that a real bounded sequence (x_n) is Cesàro convergent to ℓ if and only if the sequence of averages with indices in [α^k,α^k+1) converges to ℓ for all α>1. If, in addition, the sequence (x_n) is nonnegative, then it is Cesàro convergent to 0 if and only if the same condition holds for some α>1.

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