scholarly journals Almost sure absolute continuity of Bernoulli convolutions

2010 ◽  
Vol 46 (3) ◽  
pp. 888-893 ◽  
Author(s):  
Michael Björklund ◽  
Daniel Schnellmann
Keyword(s):  
Absolute Continuity ◽  
Bernoulli Convolutions

scholarly journals Absolute continuity of complex Bernoulli convolutions

2016 ◽  
Vol 161 (3) ◽  
pp. 435-453 ◽  
Author(s):  
PABLO SHMERKIN ◽  
BORIS SOLOMYAK
Keyword(s):  
Hausdorff Dimension ◽  
Complex Plane ◽  
Absolute Continuity ◽  
Exceptional Set ◽  
Parameter Region ◽  
Absolutely Continuous ◽  
Bernoulli Convolutions ◽  
Supercritical Parameter ◽  
Self Similar

AbstractWe 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.

On the multifractal analysis of Bernoulli convolutions. II. Dimensions

1996 ◽  
Vol 82 (1-2) ◽  
pp. 397-420 ◽  
Author(s):  
François Ledrappier ◽  
Anna Porzio
Keyword(s):  
Multifractal Analysis ◽  
Bernoulli Convolutions
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