Real-variables characterization of generalized Stieltjes functions
Classical Analysis and ODEs
2010-12-06 v2 Complex Variables
Abstract
We obtain a characterization of generalized Stieltjes functions of any order \lambda > 0 in terms of inequalities for their derivatives on (0,\infty). When \lambda=1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.
Cite
@article{arxiv.0902.0065,
title = {Real-variables characterization of generalized Stieltjes functions},
author = {Alan D. Sokal},
journal= {arXiv preprint arXiv:0902.0065},
year = {2010}
}
Comments
LaTeX2e, 9 pages. Version 2 contains some improvements in the exposition suggested by a referee. To be published in Expositiones Mathematicae