A multiplicative characterization of the power means
Tom Leinster
TL;DR
This paper provides a straightforward characterization of power means of order ≥ 1, extending recent findings on p-norms to a broader class of means with potential applications in analysis.
Contribution
It introduces a simple characterization of power means of order ≥ 1, generalizing recent results on p-norms and expanding understanding of mean functions.
Findings
Characterization applies to power means of order ≥ 1
Extends recent p-norm characterizations to broader means
Simplifies understanding of power means
Abstract
A startlingly simple characterization of the p-norms has recently been found by Aubrun and Nechita (arXiv:1102.2618) and by Fernandez-Gonzalez, Palazuelos and Perez-Garcia. We deduce a simple characterization of the power means of order greater than or equal to 1.
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