Stieltjes functions of finite order and ...
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Article dans une revue scientifique: Article original
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Title :
Stieltjes functions of finite order and hyperbolic monotonicity
Author(s) :
Bondesson, Lennart [Auteur]
Umeå University = Umeå Universitet
Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Umeå University = Umeå Universitet
Simon, Thomas [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Journal title :
Transactions of the American Mathematical Society
Pages :
4201-4222
Publisher :
American Mathematical Society
Publication date :
2018-02-14
ISSN :
0002-9947
English keyword(s) :
Hyperbolic monotonicity
Stieltjes transform
Widder condition.
Stieltjes transform
Widder condition.
HAL domain(s) :
Mathématiques [math]
English 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 ...
Show more >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 truncatedLaurent 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.Show less >
Show more >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 truncatedLaurent 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.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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Submission date :
2025-01-24T14:31:16Z
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