关键词: 代函数系, 自仿测度, 共线数字集, 谱测度, 和谐对

Abstract:

Using the feature of zeropoint sets Z(μ^M,D), where μ^M,D is the Fourier transform of selfaffine measures μM,D, we discussed the spectrality and nonspectrality of the collinear digit set. We gave a method to deal with the spectrality and nonspectrality of self\|affine measures with collinear case on R³.

Key words: iterated function system(IFS), selfaffine measure, collinear digit set, spectral measure, compatible pair