1. Distributional versions of Littlewood's Tauberian theorem
- Creator:
- Estrada, Ricardo and Vindas, Jasson
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Tauberian theorem, Laplace transform, the converse of Abel's theorem, Littlewood's Tauberian theorem, Abel and Cesàro summability, distributional Tauberian theorem, and asymptotic behavior of generalized function
- Language:
- English
- Description:
- 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 summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public