On Asymptotic Expansions of Generalized Stieltjes Functions
Ημερομηνία
2015ISSN
1617-9447Source
Computational Methods and Function TheoryVolume
15Issue
1Pages
93-115Google Scholar check
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Εμφάνιση πλήρους εγγραφήςΕπιτομή
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. © 2014, Springer-Verlag Berlin Heidelberg.