Sur quelques développements en séries
The Lebesgue Constants for Borel Summation of Laplace Series.
Two valued measure and summability of double sequences
In this paper, following the methods of Connor [connor], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [moe]) to -statistical convergence and convergence in -density using a two valued measure . We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure called the (APO) condition, inspired by the (APO) condition of Connor [jc]. We mainly investigate...
Two-sided averages for which oscillation fails.
Ueber die Gauss'sche hypergeometrische Reihe
Ueber die höheren hypergeometrischen Reihen, insbesondere über die Reihe: .................................
Ueber die ungleimässigen Convergenz und die gliedweise Integration der Reihen
Vector series whose lacunary subseries converge
The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series in a topological vector space X is called ℒ-convergent if each of its lacunary subseries (i.e. those with ) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence...
-statistically convergent function sequences
In the present paper we are concerned with convergence in -density and -statistical convergence of sequences of functions defined on a subset of real numbers, where is a finitely additive measure. Particularly, we introduce the concepts of -statistical uniform convergence and -statistical pointwise convergence, and observe that -statistical uniform convergence inherits the basic properties of uniform convergence.
О выборе подсистемы сходимости с логарифмической плотностью из произвольной ортонормированной системы
О множестве сумм условно сходящегося функционального ряда
О перестановках условно сходящихся функциональных рядов
Об одном методе суммирования функциональных рядов