Bernoulli卷积测度的谱性质

Spectral property of the Bernoulli convolutions

通过考虑2个函数,τb1(x)=λ(x-b1),τb2(x)=λ(x+b2),B={b1,b2},λ∈(0,1),研究由Bernoulli迭代函数系产生的吸引子的卷积测度的某种谱的性质,给出了当λ∈(1/2,1)∩Q时,谱测度γλ的Fourier变换的性质以及一些条件下集合Λr的正交性.

Certain spectral properties of the Bernoulli convolution measures which arise from affine iterated function systems on R,two functions： τb2（x） = λ（x ＋ b2）,τb1（x） = λ（x-b1） B = { b1,b2} λ ∈（0,1） were considered,some Fourier transform properties of γλ and the orthogonally of Λr were given in the case of λ∈（1/2,1） ∩Q.