Real-variables characterization of generalized Stieltjes functions

Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    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
    Volume28
    Issue number2
    DOIs
    StatePublished - 2010

    Fingerprint

    Stieltjes Functions
    Generalized Functions
    Derivative

    Keywords

    • 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

    • Mathematics(all)

    Cite this

    Real-variables characterization of generalized Stieltjes functions. / Sokal, Alan D.

    In: Expositiones Mathematicae, Vol. 28, No. 2, 2010, p. 179-185.

    Research output: Contribution to journalArticle

    @article{f1e0a393b8854f41bca4749077ef7df9,
    title = "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, ∞). When λ = 1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.",
    keywords = "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",
    author = "Sokal, {Alan D.}",
    year = "2010",
    doi = "10.1016/j.exmath.2009.06.004",
    language = "English (US)",
    volume = "28",
    pages = "179--185",
    journal = "Expositiones Mathematicae",
    issn = "0723-0869",
    publisher = "Urban und Fischer Verlag Jena",
    number = "2",

    }

    TY - JOUR

    T1 - Real-variables characterization of generalized Stieltjes functions

    AU - Sokal, Alan D.

    PY - 2010

    Y1 - 2010

    N2 - 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.

    AB - 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.

    KW - Bernstein-Hausdorff-Widder theorem

    KW - Completely monotone function

    KW - Completely monotone sequence

    KW - Generalized Stieltjes function

    KW - Generalized Stieltjes transform

    KW - Hausdorff moment problem

    KW - Laplace transform

    KW - Stieltjes function

    KW - Stieltjes transform

    UR - http://www.scopus.com/inward/record.url?scp=77950338440&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=77950338440&partnerID=8YFLogxK

    U2 - 10.1016/j.exmath.2009.06.004

    DO - 10.1016/j.exmath.2009.06.004

    M3 - Article

    VL - 28

    SP - 179

    EP - 185

    JO - Expositiones Mathematicae

    JF - Expositiones Mathematicae

    SN - 0723-0869

    IS - 2

    ER -