Absolute continuity of complex Bernoulli convolutions

Pablo Shmerkin; Boris Solomyak

doi:10.1017/S0305004116000335

Absolute continuity of complex Bernoulli convolutions

Pablo Shmerkin, Boris Solomyak

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.

Original language	English
Pages (from-to)	435-453
Number of pages	19
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	161
Issue number	3
DOIs	https://doi.org/10.1017/S0305004116000335
State	Published - 1 Nov 2016

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/S0305004116000335

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title = "Absolute continuity of complex Bernoulli convolutions",

abstract = "We prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.",

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AB - We prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.

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DO - 10.1017/S0305004116000335

M3 - مقالة

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EP - 453

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

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Absolute continuity of complex Bernoulli convolutions

Abstract

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