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

2024/07/22 by Callewaert, Morgan, Neyt, Lenny, Vindas, Jasson · 1 citation
#11M45 #44A10 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT) #Primary 46E10 #Secondary 40E05

paper · doi:10.48550/arxiv.2407.15547

Abstract

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 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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