Wiener tauberian theorems for ultradistributions
S. Pilipović, B. Stanković (1994)
Rendiconti del Seminario Matematico della Università di Padova
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Wiener tauberian theorems for ultradistributions
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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...