Real-variables characterization of generalized Stieltjes functions

Alan D. Sokal

doi:10.1016/j.exmath.2009.06.004

Real-variables characterization of generalized Stieltjes functions

Alan D. Sokal

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	179-185
Number of pages	7
Journal	Expositiones Mathematicae
Volume	28
Issue number	2
DOIs	https://doi.org/10.1016/j.exmath.2009.06.004
State	Published - 2010

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

General Mathematics

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10.1016/j.exmath.2009.06.004

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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.}",

note = "Funding Information: This research was supported in part by U.S. National Science Foundation Grant PHY–0424082.",

year = "2010",

doi = "10.1016/j.exmath.2009.06.004",

language = "English (US)",

volume = "28",

pages = "179--185",

journal = "Expositiones Mathematicae",

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T1 - Real-variables characterization of generalized Stieltjes functions

AU - Sokal, Alan D.

N1 - Funding Information: This research was supported in part by U.S. National Science Foundation Grant PHY–0424082.

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

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DO - 10.1016/j.exmath.2009.06.004

M3 - Article

AN - SCOPUS:77950338440

SN - 0723-0869

VL - 28

SP - 179

EP - 185

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 2

ER -

Real-variables characterization of generalized Stieltjes functions

Abstract

Keywords

ASJC Scopus subject areas

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