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)

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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.

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