Absolute continuity of Bernoulli convolutions, a simple proof
type: Item
instance of: scholarly article
title: Absolute continuity of Bernoulli convolutions, a simple proof
zbMATH Open document ID: 0867.28001
author: Yuval Peres
author: B. Solomyak
published in: Mathematical Research Letters
publication date: 1997-07-06T00:00:00Z
review text: The authors give a new simplified proof that the infinite Bernoulli convolution \(\nu_\lambda\) of the measures \[ \textstyle{{1\over 2}} (\delta_{-\lambda^n}+\delta_{\lambda^n}) \] for \(n\in\mathbb{N}\) and \({1\over 2}<\lambda<1\) is absolutely continuous with \(L^2\)-density. The proof is based on differentiation techniques for measures.
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 42A61
Mathematics Subject Classification ID: 28A15
zbMATH DE Number: 913761
zbMATH Keywords: differentiation of measures
zbMATH Keywords: infinite Bernoulli convolution
zbMATH Keywords: \(L^ 2\)-density
reviewed by: Hermann Haase
MaRDI profile type: Publication
DOI: 10.4310/MRL.1996.V3.N2.A8
description: scientific article; zbMATH DE number 913761