On a space of functions with entire Laplace transforms and its connection with the optimality of the Ingham-Karamata theorem
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915333730729984 |
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| author | Callewaert, Morgan Neyt, Lenny Vindas, Jasson |
| author_facet | Callewaert, Morgan Neyt, Lenny Vindas, Jasson |
| contents | We study approximation properties of the Fréchet space of all continuously differentiable functions $τ$ such that $τ'(x)=o(1)$ and such that their Laplace transforms admit entire extensions to $\mathbb{C}$. As an application, these approximation results are combined with the open mapping theorem to show the optimality theorem for the Ingham-Karamata Tauberian theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a space of functions with entire Laplace transforms and its connection with the optimality of the Ingham-Karamata theorem Callewaert, Morgan Neyt, Lenny Vindas, Jasson Classical Analysis and ODEs Complex Variables Functional Analysis Number Theory Primary 46E10, 11M45, Secondary 40E05, 44A10 We study approximation properties of the Fréchet space of all continuously differentiable functions $τ$ such that $τ'(x)=o(1)$ and such that their Laplace transforms admit entire extensions to $\mathbb{C}$. As an application, these approximation results are combined with the open mapping theorem to show the optimality theorem for the Ingham-Karamata Tauberian theorem. |
| title | On a space of functions with entire Laplace transforms and its connection with the optimality of the Ingham-Karamata theorem |
| topic | Classical Analysis and ODEs Complex Variables Functional Analysis Number Theory Primary 46E10, 11M45, Secondary 40E05, 44A10 |
| url | https://arxiv.org/abs/2407.15547 |