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arXiv · 2505.04225

Complete monotonicity of log-functions

Rourou Ma·Julian Weigert
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Abstract

In this article we investigate the property of complete monotonicity within a special family $\mathcal{F}_s$ of functions in $s$ variables involving logarithms. The main result of this work provides a linear isomorphism between $\mathcal{F}_s$ and the space of real multivariate polynomials. This isomorphism identifies the cone of completely monotone functions with the cone of non-negative polynomials. We conclude that the cone of completely monotone functions in $\mathcal{F}_s$ is semi-algebraic. This gives a finite time algorithm to decide whether a function in $\mathcal{F}_s$ is completely monotone

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Rourou Ma, Julian Weigert. 2025-05-07. Complete monotonicity of log-functions. https://arxiv.org/abs/2505.04225

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