Real-variables characterization of generalized Stieltjes functions

Details Real-variables characterization of generalized Stieltjes functions Real-variables characterization of generalized Stieltjes functions

2009-01-31

arxiv.org/abs/0902.0065v2

Expo. Math. 28, 179-185 (2010)

Mathematics

Classical Analysis and ODEs

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

Scientific paper

10.1016/j.exmath.2009.06.004

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.

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