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arXiv · 2112.09966

An application of a moment problem to completely monotonic functions

Vladimir Jovanović·Milanka Treml
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Abstract

We consider the following question: if a function of the form $\int_0^{\infty}\varphi(t)\, e^{-xt}dt$ is completely monotonic, is it then $\varphi\ge0$? It turns out that the question is related to a moment problem. In the end we apply those results to answer some questions concerning complete monotonicity of certain functions raised in F. Qi and R. Agarwal, \textit{On complete monotonicity for several classes of functions related to ratios of gamma functions}, J. Inequal. Appl. (2019).

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Vladimir Jovanović, Milanka Treml. 2021-12-18. An application of a moment problem to completely monotonic functions. https://arxiv.org/abs/2112.09966

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