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Absolute continuity of complex Bernoulli convolutions

Published online by Cambridge University Press:  16 May 2016

PABLO SHMERKIN  and
BORIS SOLOMYAK
PABLO SHMERKIN
Affiliation:
Department of Mathematics and Statistics, Torcuato Di Tella University, and CONICET, Buenos Aires, Argentina. e-mail: [email protected]
BORIS SOLOMYAK
Affiliation:
Department of Mathematics, Bar Ilan University, Ramat–Gan, 5290002, Israel. e-mail: [email protected]
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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 parametrised families of self-similar sets and measures in the complex plane, extending earlier results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 3 , November 2016 , pp. 435 - 453
Copyright
Copyright © Cambridge Philosophical Society 2016 

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