Sixty Years of Bernoulli Convolutions
نویسنده
چکیده
The distribution νλ of the random series ∑ ±λ is the infinite convolution product of 1 2 (δ−λn + δλn). These measures have been studied since the 1930’s, revealing connections with harmonic analysis, the theory of algebraic numbers, dynamical systems, and Hausdorff dimension estimation. In this survey we describe some of these connections, and the progress that has been made so far on the fundamental open problem: For which λ ∈ ( 1 2 , 1) is νλ absolutely continuous? Our main goal is to present an exposition of results obtained by Erdős, Kahane and the authors on this problem. Several related unsolved problems are collected at the end of the paper.
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