%0 Journal Article
%T 三元数字集的自相似测度的谱性性质<br>Spectrality of Self-Similar Measures with Three Element Digit Sets
%A 曹永申
%J Pure Mathematics
%P 218-232
%@ 2160-7605
%D 2022
%I Hans Publishing
%R 10.12677/PM.2022.121026
%X <div style=\"text-align:justify;\">
	Fu和Wen证明了压缩比为实数ρ和有界三元整数字集列D<sub>n</sub>={0, a<sub>n</sub>,b<sub>n</sub>}？？生成的无穷Bernoulli 卷积测度是谱测度的充要条件.本文研究由压缩比为实数ρ和三元实数字集D定义的迭代函数系统生成的自相似测度的谱性质, 我们证明该测度是谱测度当且仅当ρ<sup>？1</sup>是以3为因子的非零整数且存在非零实数a, 使得a(D？α)模3同余集合{0,1,2}, 其中α∈D 。<br />
Fu and Wen prove that the convolution of the infinite Bernoulli measure generated by the compression ratio of real numbers ρ and the sequence of bounded three-element integers D<sub>n</sub>={0, a<sub>n</sub>,b<sub>n</sub>}？？ is a sufficient and necessary condition for spectral measure. In this paper we study the spectrality of the self-similar measure generated by the iterative function system defined by the compression ratio of real numbers ρ and the set of three-element real digits D . We prove that the measure is spectral if and only if ρ<sup>？1</sup> is a non-zero integer with a factor of&nbsp; 3 and a(D？α) is congruence with {0,1,2} under (mod 3) for some a, where α∈D.
</div>
%K 自相似测度，谱测度，谱，Fourier 变换<br>Self-Similar Measure
%K Spectral Measure
%K Spectrum
%K Fourier Transform
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=48374