Geodesic
Distributional versions of Littlewood's Tauberian theorem
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 403-420 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
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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     title = {Distributional versions of {Littlewood's} {Tauberian} theorem},
     journal = {Czechoslovak Mathematical Journal},
     pages = {403--420},
     year = {2013},
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     language = {en},
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Estrada, Ricardo; Vindas, Jasson. Distributional versions of Littlewood's Tauberian theorem. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 403-420. doi: 10.1007/s10587-013-0025-1

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