Bernoulli convolutions with Garsia parameters in (1,√2] have continuous density functions

Yu, Han

doi:10.1090/proc/15971

Bernoulli convolutions with Garsia parameters in $(1,\sqrt {2}]$ have continuous density functions
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Proc. Amer. Math. Soc. 150 (2022), 4359-4368 Request permission

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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