Generalized Stieltjes transforms: basic aspects
Classical Analysis and ODEs
2012-02-14 v2 Complex Variables
Abstract
The paper surveys the basic properties of generalized Stieltjes functions including some new ones. We introduce the notion of the exact Stieltjes order and give a criterion of exactness, simple sufficient conditions and some prototypical examples. The paper includes an appendix, where we define the left sided Riemann-Liouville and the right sided Kober-Erdelyi fractional integrals of measures supported on half axis and give inversion formulas for them.
Cite
@article{arxiv.1111.4271,
title = {Generalized Stieltjes transforms: basic aspects},
author = {Dmitry Karp and Elena Prilepkina},
journal= {arXiv preprint arXiv:1111.4271},
year = {2012}
}
Comments
23 pages, no figures; a counterexample related to complex variable chracterization added; some typos corrected, other minore improvements made