English

An application of a moment problem to completely monotonic functions

Classical Analysis and ODEs 2021-12-21 v1

Abstract

We consider the following question: if a function of the form 0φ(t)extdt\int_0^{\infty}\varphi(t)\, e^{-xt}dt is completely monotonic, is it then φ0\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).

Keywords

Cite

@article{arxiv.2112.09966,
  title  = {An application of a moment problem to completely monotonic functions},
  author = {Vladimir Jovanović and Milanka Treml},
  journal= {arXiv preprint arXiv:2112.09966},
  year   = {2021}
}