On Generalized Stieltjes Functions
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On Generalized Stieltjes Functions. / Koumandos, Stamatis; Pedersen, Henrik L.
In: Constructive Approximation, Vol. 50, No. 1, 2019, p. 129-144.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - On Generalized Stieltjes Functions
AU - Koumandos, Stamatis
AU - Pedersen, Henrik L.
PY - 2019
Y1 - 2019
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=85048833704&partnerID=8YFLogxK
U2 - 10.1007/s00365-018-9440-8
DO - 10.1007/s00365-018-9440-8
M3 - Journal article
AN - SCOPUS:85048833704
VL - 50
SP - 129
EP - 144
JO - Constructive Approximation
JF - Constructive Approximation
SN - 0176-4276
IS - 1
ER -
ID: 203596168