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

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 Added by Han Yu
 Publication date 2021
  fields
and research's language is English
 Authors Han Yu




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Let $lambdain (1,sqrt{2}]$ 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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