Distributional versions of Littlewood's Tauberian theorem

Estrada, Ricardo ; Vindas, Jasson

Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 403-420

Abstract (VO)

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.

Détail

DOI : 10.1007/s10587-013-0025-1

Classification : 40E05, 40G05, 40G10, 44A10, 46F12, 46F20
Keywords: Tauberian theorem; Laplace transform; the converse of Abel's theorem; Littlewood's Tauberian theorem; Abel and Cesàro summability; distributional Tauberian theorem; asymptotic behavior of generalized function

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