Karamata's theorem for regularised Cauchy transforms
Complex Variables
2025-09-12 v3
Abstract
We prove Abelian and Tauberian theorems for regularised 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 regularised Cauchy transform.
Cite
@article{arxiv.2307.12249,
title = {Karamata's theorem for regularised Cauchy transforms},
author = {Matthias Langer and Harald Woracek},
journal= {arXiv preprint arXiv:2307.12249},
year = {2025}
}