Real Analysis Exchange

On Inhomogeneous Bernoulli Convolutions and Random Power Series

Antonios Bisbas and Jörg Neunhäuserer

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Abstract

We extend the results of Peres and Solomyak on absolute continuity and singularity of homogeneous Bernoulli convolutions to inhomogeneous ones and generalize the result to random power series given by inhomogeneous Markov chains. In addition we prove an Erd\"{o}s-Salem type theorem for inhomogeneous Bernoulli convolutions.

Article information

Source
Real Anal. Exchange, Volume 36, Number 1 (2010), 213-222.

Dates
First available in Project Euclid: 14 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.rae/1300108094

Mathematical Reviews number (MathSciNet)
MR3016413

Zentralblatt MATH identifier
1247.26017

Subjects
Primary: 26A46: Absolutely continuous functions 26A30: Singular functions, Cantor functions, functions with other special properties
Secondary: 28A80: Fractals [See also 37Fxx] 28A78: Hausdorff and packing measures 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure

Keywords
inhomogeneous Bernoulli convolution random power series absolute continuity singularity Pisot numbers

Citation

Bisbas, Antonios; Neunhäuserer, Jörg. On Inhomogeneous Bernoulli Convolutions and Random Power Series. Real Anal. Exchange 36 (2010), no. 1, 213--222. https://projecteuclid.org/euclid.rae/1300108094


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