Karamata's theorem for regularized Cauchy transforms

Langer, Matthias and Woracek, Harald (2024) Karamata's theorem for regularized Cauchy transforms. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. pp. 1-61. ISSN 0308-2105 (https://doi.org/10.1017/prm.2023.128)

[thumbnail of Langer-Woracek-PRSEA-2024-Karamatas-theorem-for-regularised-Cauchy]
Preview
 Text. Filename: Langer-Woracek-PRSEA-2024-Karamatas-theorem-for-regularised-Cauchy.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo
Download (567kB)| Preview

Abstract

We prove Abelian and Tauberian theorems for regularized Cauchy transforms of positive Borel measures on the real line whose distribution functions grow at most polynomially at infinity. In particular, we relate the asymptotics of the distribution functions to the asymptotics of the regularized Cauchy transform.

ORCID iDs

Langer, Matthias ORCID logoORCID: https://orcid.org/0000-0001-8813-7914 and Woracek, Harald;
CORE (COnnecting REpositories)