On Asymptotic Expansions of Generalized Stieltjes Functions

On Asymptotic Expansions of Generalized Stieltjes Functions

We characterize the generalized Stieltjes functions corresponding to measures on the positive real axis having moments of all orders in terms of monotonicity properties of the remainders in asymptotic expansions of these functions. A special case furnishes a half line analogue of a classical theorem...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Computational methods and function theory 2015-03, Vol.15 (1), p.93-115
Hauptverfasser: Koumandos, Stamatis, Pedersen, Henrik Laurberg
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We characterize the generalized Stieltjes functions corresponding to measures on the positive real axis having moments of all orders in terms of monotonicity properties of the remainders in asymptotic expansions of these functions. A special case furnishes a half line analogue of a classical theorem of Hamburger and Nevanlinna about asymptotic expansions of Cauchy transforms of measures having moments of all orders.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-014-0094-7