TY - JOUR
T1 - On Generalized Stieltjes Functions
AU - Koumandos, Stamatis
AU - Pedersen, Henrik L.
PY - 2019/8/15
Y1 - 2019/8/15
N2 - It is shown that a function f is a generalized Stieltjes function of order λ> 0 if and only if x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≥ 0 , thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions f for which x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≤ n 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 λ> 0 if and only if x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≥ 0 , thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions f for which x1-λ(xλ-1+kf(x))(k) is completely monotonic for all k≤ n 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
SN - 0176-4276
VL - 50
SP - 129
EP - 144
JO - Constructive Approximation
JF - Constructive Approximation
IS - 1
ER -