A Tauberian theorem for the Ingham summation method
Vytas Zacharovas (2011)
Acta Arithmetica
Similarity:
Vytas Zacharovas (2011)
Acta Arithmetica
Similarity:
Ferenc Móricz (2000)
Studia Mathematica
Similarity:
Given ⨍ ∈ , 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...
C.T. Rajagopal (1954)
Mathematische Zeitschrift
Similarity:
C.T. Rajagopal (1952/53)
Mathematische Zeitschrift
Similarity:
T. Pati (1954/55)
Mathematische Zeitschrift
Similarity:
Mangalam R. Parameswaran (1975)
Mathematische Zeitschrift
Similarity:
Gordon M. Petersen (1962)
Mathematische Zeitschrift
Similarity:
K. Anjaneyulu (1966)
Mathematische Zeitschrift
Similarity:
M. S. Rangachari (1969)
Colloquium Mathematicae
Similarity:
Y. Sitaraman (1968)
Mathematische Zeitschrift
Similarity:
Ricardo Estrada, Jasson Vindas (2013)
Czechoslovak Mathematical Journal
Similarity:
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...
David Seifert (2015)
Studia Mathematica
Similarity:
The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a certain boundary function, with the quality of the estimate depending on the degree of smoothness this boundary function is assumed to possess. The result is then used to give a new proof of the quantified Katznelson-Tzafriri theorem recently obtained by...