Functional Analysis Seminar

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Past events in this series
8 May 2018

We consider a vector-valued function $f: \mathbb{R}_+ \to X$ which is locally of bounded variation and give a decay rate for $|A(t)|$ for increasing $t$ under certain conditions on the Laplace-Stieltjes transform $\widehat{dA}$ of $A$. For this, we use a Tauberian condition inspired by the work of Ingham and Karamata and a contour integration method invented by Newman. Our result is a generalisation of already known Tauberian theorems for bounded functions and is applicable to Dirichlet series. We will say something about the connection between the obtained decay rates and number theory.

  • Functional Analysis Seminar
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