Statistical extensions of some classical Tauberian theorems in nondiscrete setting

Ferenc Móricz

Displaying similar documents to “Statistical extensions of some classical Tauberian theorems in nondiscrete setting”

Ordinary convergence follows from statistical summability (C,1) in the case of slowly decreasing or oscillating sequences

Ferenc Móricz (2004)

Colloquium Mathematicae

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Schmidt’s Tauberian theorem says that if a sequence (xk) of real numbers is slowly decreasing and $l i m_{n \to \infty} (1 / n) \sum_{k = 1}^{n} x_{k} = L$ , then $l i m_{k \to \infty} x_{k} = L$ . The notion of slow decrease includes Hardy’s two-sided as well as Landau’s one-sided Tauberian conditions as special cases. We show that ordinary summability (C,1) can be replaced by the weaker assumption of statistical summability (C,1) in Schmidt’s theorem. Two recent theorems of Fridy and Khan are also corollaries of our Theorems 1 and 2. In the Appendix, we present a new proof...

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...

A Tauberian theorem for the Ingham summation method

Vytas Zacharovas (2011)

Acta Arithmetica

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Tauberian Retrieval Theory

Časlav V. Stanojević, Vera B. Stanojević (2002)

Publications de l'Institut Mathématique

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Summability of double sequences by weighted mean methods and Tauberian conditions for convergence in Pringsheim's sense.

Móricz, Ferenc, Stadtmüller, U. (2004)

International Journal of Mathematics and Mathematical Sciences

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On a Tauberian theorem of Keldysh.

Grishin, A.F., Poedintseva, I.V. (2004)

Zapiski Nauchnykh Seminarov POMI

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A Generalization of Tauber's Theorem and some Tauberian Constants.

C.T. Rajagopal (1952/53)

Mathematische Zeitschrift

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A Generalization of Tauber's Theorem and some Tauberian Constants (II).

C.T. Rajagopal (1954)

Mathematische Zeitschrift

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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...