Riesz products on the ring of dyadic integers
type: Item
instance of: scholarly article
title: Riesz products on the ring of dyadic integers
zbMATH Open document ID: 1169.28002
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-06-23T00:00:00Z
review text: In this paper a class of Riesz products on the ring of dyadic integers is introduced. Using almost everywhere convergence of certain series, Hausdorff dimension of these Riesz products is determined. Other properties, such as mutually absolute continuity, quasi-invariance and quasi-Bernoulli property, are also discussed. In the previous paper [C. R., Math., Acad. Sci. Paris 344, No. 7, 425--430 (2007; Zbl 1169.28001)] \textit{A. Fan} and the author introduced a class of probability measures, called Riesz products, on the ring \(\mathbb Z_p\) of \(p\)-adic integers. They proved a result on the almost everywhere convergence, with respect to a Riesz product, of some related series and then obtained the Hausdorff dimension of the Riesz product.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 28A33
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 11S80
Mathematics Subject Classification ID: 43A75
zbMATH DE Number: 5568974
zbMATH Keywords: Riesz products
zbMATH Keywords: ring of dyadic integers
zbMATH Keywords: lacunary series
zbMATH Keywords: Hausdorff dimension
author: Xiong-Ying Zhang
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.03.067
OpenAlex ID: W2971296084
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DOI: 10.1016/J.JMAA.2009.03.067
description: scientific article; zbMATH DE number 5568974