On Generalized Stieltjes Functions

Stamatis Koumandos; Henrik L. Pedersen

doi:10.1007/s00365-018-9440-8

On Generalized Stieltjes Functions

Stamatis Koumandos, Henrik L. Pedersen^*

^*Corresponding author for this work

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

It is shown that a function f is a generalized Stieltjes function of order (Formula presented.) if and only if (Formula presented.) is completely monotonic for all (Formula presented.), thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions f for which (Formula presented.) is completely monotonic for all (Formula presented.) is obtained in terms of properties of the representing measure of f.

Original language	English
Journal	Constructive Approximation
Volume	50
Issue number	1
Pages (from-to)	129-144
ISSN	0176-4276
DOIs	https://doi.org/10.1007/s00365-018-9440-8
Publication status	Published - 2019

Keywords

Completely monotonic function
Generalized Stieltjes function
Laplace transform

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10.1007/s00365-018-9440-8

OAvers-On generalized Stieltjes functionsAccepted author manuscript, 286 KB

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AB - It is shown that a function f is a generalized Stieltjes function of order (Formula presented.) if and only if (Formula presented.) is completely monotonic for all (Formula presented.), thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions f for which (Formula presented.) is completely monotonic for all (Formula presented.) is obtained in terms of properties of the representing measure of f.

KW - Completely monotonic function

KW - Generalized Stieltjes function

KW - Laplace transform

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DO - 10.1007/s00365-018-9440-8

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JF - Constructive Approximation

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ER -

On Generalized Stieltjes Functions

Abstract

Keywords

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