平面特定四元素集自仿测度的谱与非谱性  

Spectrality and Non-spectral Properties of Self-affine Measure of the Plane Specific Four Elements Set

作　　者：刘岩[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710119

出　　处：《西安文理学院学报（自然科学版）》2017年第2期1-6,共6页Journal of Xi’an University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11571214)

摘　　要：设μ_(M,D)是由扩张矩阵M∈M_n(Z)和有限数字集DZ^n通过仿射迭代函数系{φ_d(x)=M^(-1)(x+d)}_(d∈D)唯一确定的自仿测度.平面上三元素集自仿测度μ_(M,D)的谱与非谱性已得到完全的解决,但平面上四元素集自仿测度μ_(M,D)的谱性与非谱性并没有完全解决.文中针对平面特定四元素集自仿测度的谱与非谱性得到一些结果.Let μM,Dbe the self-affine measure uniquely determined by an expanding matrix M∈M_n（Z） and a finitedigit set D  Z^nthrough the affine iterated function system（IFS）{ φd（x） = M^-1（x ＋ d） }d∈D. The spectrality and non-spectral properties of self-affine measure of the plane three elements set have been completely solved,but the spectrality and non-spectral properties of self-affine measure of the plane specific four elements set have not been completely solved. In this paper,some results are obtained for the spectral and non-spectral properties of self-affine measure of the planar four elements set.

关 键 词：自仿测度 谱测度 和谐对 谱性质 

分 类 号：O174.2[理学—数学]