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

We study approximation properties of the Fréchet space of all continuously differentiable functions $\tau$ such that ${\tau }^{\prime }(x)=o(1)$ and such that their Laplace transforms admit entire e…