Pre stieltjes functions

Henrik Laurberg Pedersen

doi:10.1007/s00009-010-0043-2

Pre stieltjes functions

5 Citationer (Scopus)

Abstract

In this paper we characterize the class C_k of functions f on (0,∞) for which f(x), . . ., (x^kf(x))^(k) are completely monotonic for given k. In the limit we obtain the well-known characterization of the class of Stieltjes functions as those functions f defined on the positive half line for which (x^kf(x))^(k) is completely monotonic on (0,∞) for all k ≥ 0.

Originalsprog	Engelsk
Tidsskrift	Mediterranean Journal of Mathematics
Vol/bind	8
Udgave nummer	1
Sider (fra-til)	113-122
Antal sider	10
ISSN	1660-5446
DOI	https://doi.org/10.1007/s00009-010-0043-2
Status	Udgivet - mar. 2011

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10.1007/s00009-010-0043-2

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AB - In this paper we characterize the class Ck of functions f on (0,∞) for which f(x), . . ., (xkf(x))(k) are completely monotonic for given k. In the limit we obtain the well-known characterization of the class of Stieltjes functions as those functions f defined on the positive half line for which (xkf(x))(k) is completely monotonic on (0,∞) for all k ≥ 0.

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DO - 10.1007/s00009-010-0043-2

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JO - Mediterranean Journal of Mathematics

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Pre stieltjes functions

Abstract

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