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arXiv · 1201.1408

Distributional versions of Littlewood's Tauberian theorem

Ricardo Estrada·Jasson Vindas
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Abstract

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series where Ces\`{a}ro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.

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Ricardo Estrada, Jasson Vindas. 2012-01-06. Distributional versions of Littlewood's Tauberian theorem. https://doi.org/10.1007/s10587-013-0025-1

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