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arXiv · 2407.15547

On a space of functions with entire Laplace transforms and its connection with the optimality of the Ingham-Karamata theorem

Morgan Callewaert·Lenny Neyt·Jasson Vindas
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Abstract

We study approximation properties of the Fr\'{e}chet space of all continuously differentiable functions $\tau$ such that $\tau'(x)=o(1)$ 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.

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Morgan Callewaert, Lenny Neyt, Jasson Vindas. 2024-07-22. On a space of functions with entire Laplace transforms and its connection with the optimality of the Ingham-Karamata theorem. https://doi.org/10.1007/s11785-025-01704-8

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