Real-variables characterization of generalized Stieltjes functions
classification
🧮 math.CA
math.CV
keywords
characterizationfunctionsstieltjesgeneralizedlambdaderivativesfirstinequalities
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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.
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