Real-variables characterization of generalized Stieltjes functions

Abstract

We obtain a characterization of generalized Stieltjes functions of any order λ> 0 in terms of inequalities for their derivatives on (0,\infty). When λ=1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.

LaTeX2e, 9 pages. Version 2 contains some improvements in the exposition suggested by a referee. To be published in Expositiones Mathematicae

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