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

2021/08/02 by Yu, Han
#28A78 #37A45 #42A85 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2108.01008

Abstract

Let λ∈ (1,√(2)] be an algebraic integer with Mahler measure 2. A classical result of Garsia shows that the Bernoulli convolution μ_λ is absolutely continuous with respect to the Lebesgue measure with a density function in L^∞. In this paper, we show that the density function is continuous.

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