一类Moran测度的傅里叶变换的衰减率

A Class of Decay Rate of FourierTransform of Moran Measure

摘要: 设0<ρ<1,其中ρ=q/p, gcd(p,q)=1且q > 1，{D_n}_n=1^∞是有界且满足∩_n=1^∞(D_n-D_n)\{0}≠∅.在这篇论文中，我们研究ℝ上具有紧支撑的Borel概率测度

Abstract: μ_ρ,D_n=δ_ρD₁*δ_ρ²D₂*…，的傅里叶变换的衰减率,结果表明,满足以上条件的Moran测度μ_ρ,D_n。的傅里叶变换的衰减率是对数形式的。Let 0<ρ<1,where ρ=q/p, gcd(p,q)=1 andq > 1, {D_n}_n=1^∞ is bounded and satisfy ∩_n=1^∞(D_n-D_n)\{0}≠∅. In this paper, we study the decay rate of Fourier transform of a Borel probability measure with compact support on ℝ μ_ρ,D_n=δ_ρD₁*δ_ρ²D₂*…. It is shown that a class of the decay rate of the Fourier transform of Moran measure μ_ρ,D_n is logarithmic.