Almost sure convergence of weighted series of contractions
type: Item
instance of: scholarly article
title: Almost sure convergence of weighted series of contractions
zbMATH Open document ID: 1024.28015
published in: Illinois Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: The authors investigate the pointwise convergence of randomly weighted series of contractions \(\sum_{k=1}^{\infty}W_k(\omega)T^{p_k}\) . The functions \(W_k\) form a sequence of independent, mean zero, square integrable variables defined on the probability measure space and \(T\) is a linear contraction on \(L^2(\mu)\). The sequence \(p_k\) of non-negative integers is non-decreasing. They provide a sufficient condition that guarantees the ``universal'' a.e. convergence of such randomly generated series. The universality comes from the fact that they can find a set of \(\omega\) of full measure for which the series converges a.e for any contraction \(T\). The method is based on some extension of Salem and Zygmund classical results providing uniform estimates for random polynomials.
reviewed by: Idris Assani
Mathematics Subject Classification ID: 28D99
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G12
zbMATH DE Number: 1839929
zbMATH Keywords: weighted series
zbMATH Keywords: random polynomials
zbMATH Keywords: pointwise convergence
zbMATH Keywords: contractions
author: Fakhreddine Boukhari
author: Michel Weber
MaRDI profile type: Publication
Recommended article: Q5414391
Recommended article: Q4882283
Recommended article: Almost sure convergence of weighted partial sums
Recommended article: Convergence presque sûre de séries à poids aléatoires
Recommended article: A remark on almost sure convergence of weighted sums
Recommended article: On the strong convergence of weighted sums
Recommended article: On the strong convergence of a weighted sum
description: scientific article; zbMATH DE number 1839929