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arXiv · 1504.00631

Absolute continuity of complex Bernoulli convolutions

Pablo Shmerkin·Boris Solomyak
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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 parametrized families of self-similar sets and measures in the complex plane, extending earlier results.

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Pablo Shmerkin, Boris Solomyak. 2015-04-02. Absolute continuity of complex Bernoulli convolutions. https://doi.org/10.1017/s0305004116000335

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