Real-variables characterization of generalized Stieltjes functions

Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review


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

    Original languageEnglish (US)
    Pages (from-to)179-185
    Number of pages7
    JournalExpositiones Mathematicae
    Issue number2
    StatePublished - 2010


    • Bernstein-Hausdorff-Widder theorem
    • Completely monotone function
    • Completely monotone sequence
    • Generalized Stieltjes function
    • Generalized Stieltjes transform
    • Hausdorff moment problem
    • Laplace transform
    • Stieltjes function
    • Stieltjes transform

    ASJC Scopus subject areas

    • General Mathematics


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