Tauberian conditions for absolute convergence.

P. Chandra

Displaying similar documents to “Tauberian conditions for absolute convergence.”

Distributional versions of Littlewood's Tauberian theorem

Ricardo Estrada, Jasson Vindas (2013)

Czechoslovak Mathematical Journal

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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...

Tauberian conditions for $L^{1}$ -convergence of modified complex trigonometric sums.

Kaur, Kulwinder (2003)

Lobachevskii Journal of Mathematics

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Tauberian theorems for Cesàro summable double integrals over $ℝ_{+}^{2}$

Ferenc Móricz (2000)

Studia Mathematica

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Given ⨍ ∈ $L_{l}^{1} o c (ℝ_{+}^{2})$ , denote by s(w,z) its integral over the rectangle [0,w]× [0,z] and by σ(u,v) its (C,1,1) mean, that is, the average value of s(w,z) over [0,u] × [0,v], where u,v,w,z>0. Our permanent assumption is that (*) σ(u,v) → A as u,v → ∞, where A is a finite number. First, we consider real-valued functions ⨍ and give one-sided Tauberian conditions which are necessary and sufficient in order that the convergence (**) s(u,v) → A as u,v → ∞ follow from (*). Corollaries allow these...