中文摘要：

设μM,D是由扩张矩阵M∈Mn（Z）和有限数字集DZ^n通过仿射迭代函数系{φd（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μM,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.

英文摘要：

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.