Corpus ID: 236772912

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

  title={Bernoulli convolutions with Garsia parameters in \$(1,\sqrt\{2\}]\$ have continuous density functions},
  author={Han Yu},
  • Han Yu
  • Published 2021
  • Mathematics
Let λ ∈ (1, √ 2] be an algebraic integer with Mahler measure 2. A classical result of Garsia shows that the Bernoulli convolution μλ 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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