Stieltjes functions of finite order and hyperbolic monotonicity

Bondesson, Lennart; Simon, Thomas

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1090/tran/7123

Title :

Stieltjes functions of finite order and hyperbolic monotonicity

Author(s) :

Bondesson, Lennart [Auteur]
Umeå University, Sweden
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.

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 >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

1604.05267
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