Langer, M., & Woracek, H. (2024). Karamata’s theorem for regularized Cauchy transforms. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1–61. https://doi.org/10.1017/prm.2023.128
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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Project title:
Nichtlineare Wellengleichungen und Krein–de Branges-Theorie: I 4600 (FWF - Österr. Wissenschaftsfonds)
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