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Discrete limit theorems for the Laplace transform of the Riemann zeta-function

Roma Kačinskaitė, Antanas Laurinčikas (2005)

Acta Mathematica Universitatis Ostraviensis

In the paper discrete limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Laplace transform of the Riemann zeta-function are proved.

Distributional versions of Littlewood's Tauberian theorem

Ricardo Estrada, Jasson Vindas (2013)

Czechoslovak Mathematical Journal

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel...

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