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Karamata's theorem for regularized Cauchy transforms
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Matthias Langer, Harald Woracek
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View

Published online by Cambridge University Press:

26 January 2024, pp. 1-61
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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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Karamata's theorem for regularized Cauchy transforms