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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.12249 |
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| _version_ | 1866911148276711424 |
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| author | Langer, Matthias Woracek, Harald |
| author_facet | Langer, Matthias Woracek, Harald |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12249 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Karamata's theorem for regularised Cauchy transforms Langer, Matthias Woracek, Harald Complex Variables 30E20, 40E05, 26A12 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. |
| title | Karamata's theorem for regularised Cauchy transforms |
| topic | Complex Variables 30E20, 40E05, 26A12 |
| url | https://arxiv.org/abs/2307.12249 |