Real-variables characterization of generalized Stieltjes functions

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Sokal, Alan D.
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Abstract
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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.
Comment: LaTeX2e, 9 pages. Version 2 contains some improvements in the exposition suggested by a referee. To be published in Expositiones Mathematicae
Keywords
Mathematics - Classical Analysis and ODEs, Mathematics - Complex Variables, 26A48 (Primary), 26D10, 30E05, 30E20, 44A10, 44A15, 44A60 (Secondary)
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