A general quantified Ingham-Karamata Tauberian theorem
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910686716624896 |
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| author | Debruyne, Gregory |
| author_facet | Debruyne, Gregory |
| contents | We provide a general quantified Ingham-Karamata Tauberian theorem with a flexible one-sided Tauberian condition under several types of boundary behavior for the Laplace transform. Our results in particular improve a theorem by Stahn, removing a vexing restriction on the growth of the Laplace transform. Improving existing optimality results, we also show that the obtained quantified rate is optimal in almost all cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A general quantified Ingham-Karamata Tauberian theorem Debruyne, Gregory Classical Analysis and ODEs Complex Variables Number Theory Primary 40E05, Secondary 11M45, 44A10 We provide a general quantified Ingham-Karamata Tauberian theorem with a flexible one-sided Tauberian condition under several types of boundary behavior for the Laplace transform. Our results in particular improve a theorem by Stahn, removing a vexing restriction on the growth of the Laplace transform. Improving existing optimality results, we also show that the obtained quantified rate is optimal in almost all cases. |
| title | A general quantified Ingham-Karamata Tauberian theorem |
| topic | Classical Analysis and ODEs Complex Variables Number Theory Primary 40E05, Secondary 11M45, 44A10 |
| url | https://arxiv.org/abs/2411.03809 |