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Stieltjes functions of finite order and hyperbolic monotonicity
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2018 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 370, no 6, p. 4201-4222Article in journal (Refereed) Published
Abstract [en]

A class of Stieltjes functions of finite type is introduced. These satisfy Widder's conditions on the successive derivatives up to some finite order and are not necessarily smooth. We show that such functions have a unique integral representation along some generic kernel which is a truncated Laurent series approximating the standard Stieltjes kernel. We then obtain a two-to-one correspondence, via the logarithmic derivative, between these functions and a subclass of hyperbolically monotone functions of finite type. This correspondence generalizes a representation of HCM functions in terms of two Stieltjes transforms earlier obtained by the first author.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2018. Vol. 370, no 6, p. 4201-4222
Keywords [en]
Hyperbolic monotonicity, Stieltjes transform, Widder condition
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-148624DOI: 10.1090/tran/7123ISI: 000428311400017OAI: oai:DiVA.org:umu-148624DiVA, id: diva2:1224117
Available from: 2018-06-26 Created: 2018-06-26 Last updated: 2018-06-26Bibliographically approved

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Bondesson, Lennart

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