Distributional versions of Littlewood's Tauberian theorem

Details Distributional versions of Littlewood's Tauberian theorem Distributional versions of Littlewood's Tauberian theorem

2012-01-06

arxiv.org/abs/1201.1408v1

Mathematics

Functional Analysis

15 pages

Scientific paper

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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