Vilenkin–Lebesgue Points and Almost Everywhere Convergence for Some Classical Summability Methods
Nato Nadirashvili, Lars‐Erik Persson, George Tephnadze, Ferenc Weisz
Abstract
Abstract The concept of Vilenkin–Lebesgue points was introduced in [12], where the almost everywhere convergence of Fejer means of Vilenkin–Fourier series was proved. In this paper, we present a different (and simpler) approach to prove a similar result, which can be used to prove that the corresponding result holds also in a more general context, namely for regular Norlund and T -means.
Topics & Concepts
MathematicsAlmost everywhereLebesgue integrationConvergence (economics)Fourier seriesContext (archaeology)Pure mathematicsDominated convergence theoremApplied mathematicsMathematical analysisRate of convergenceConvergence testsElectrical engineeringEngineeringPaleontologyChannel (broadcasting)Economic growthBiologyEconomicsApproximation Theory and Sequence SpacesAdvanced Harmonic Analysis ResearchDifferential Equations and Boundary Problems