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arXiv · 2108.01008

Bernoulli convolutions with Garsia parameters in $(1,\sqrt{2}]$ have continuous density functions

Han Yu
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Abstract

Let $\lambda\in (1,\sqrt{2}]$ be an algebraic integer with Mahler measure $2.$ A classical result of Garsia shows that the Bernoulli convolution $\mu_\lambda$ is absolutely continuous with respect to the Lebesgue measure with a density function in $L^\infty$. In this paper, we show that the density function is continuous.

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Han Yu. 2021-08-02. Bernoulli convolutions with Garsia parameters in $(1,\sqrt{2}]$ have continuous density functions. https://arxiv.org/abs/2108.01008

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