Spectra of Bernoulli Convolutions
نویسندگان
چکیده
منابع مشابه
On the Gibbs properties of Bernoulli convolutions
We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the β-numeration. A matrix decomposition of these measures is obtained in the case when β is a PV number. We also determine their Gibbs properties for β being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.
متن کامل2 N ov 2 00 4 On the Gibbs properties of Bernoulli convolutions related to β - numeration in multinacci bases
We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the β-numeration. A matrix decomposition of these measures is obtained in the case when β is a PV number. We also determine their Gibbs properties for β being a multi-nacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.
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It is shown that the closure of the set of Fourier coefficients of the Bernoulli convolution μθ parameterized by a Pisot number θ, is countable. Combined with results of Salem and Sarnak, this proves that for every fixed θ > 1 the spectrum of the convolution operator f 7→ μθ ∗ f in L(S) (where S is the circle group) is countable and is the same for all p ∈ (1,∞), namely, {μ̂θ(n) : n ∈ Z}. Our re...
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It is shown that the closure of the set of Fourier coefficients of the Bernoulli convolution μθ parameterized by a Pisot number θ is countable. Combined with results of Salem and Sarnak, this proves that for every fixed θ > 1 the spectrum of the convolution operator f 7→ μθ∗f in L(S) (where S is the circle group) is countable and is the same for all p ∈ (1,∞), namely, {μ̂θ(n) : n ∈ Z}. Our resul...
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We consider finite Bernoulli convolutions with a parameter 1/2 < λ < 1 supported on a discrete point set, generically of size 2 . These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure νλ, as N → ∞. Numerical evidence suggests that for a generic λ, the distribution of spacings between appropriately rescaled points is Poissonian. We obtain some parti...
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