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- W1969932020 abstract "The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 1 2 <λ<1 , and singular if λ −1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convolutions ν λ such that their density functions, if they exist, are not L 2 . We also construct other Bernoulli convolutions whose density functions, if they exist, behave rather badly." @default.
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- W1969932020 date "2004-09-01" @default.
- W1969932020 modified "2023-09-28" @default.
- W1969932020 title "Bernoulli convolutions associated with certain non-Pisot numbers" @default.
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- W1969932020 doi "https://doi.org/10.1016/j.aim.2003.05.002" @default.
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