空间特定三元素数字集的自仿测度的谱与非谱性质

Spectrality and non-spectrality of a certain self-affine measures on R^3

借助谱性质与非谱性质在Z-相似变换下的不变性,利用零点集的特征,讨论了由矩阵M=p 0 00 p 00 0p和数字集D=000110011所决定的μM,D的谱与非谱性质.得出了p∈3Z\{0}时,μM,D是谱测度,否则μM,D是非谱测度,且L2(μM,D)中至多有3个相互正交的指数函数.

By use of the invarant under the Z-similarity of the spectrality and non-spectrality and the char-acteristic of the,μM,D＇s zero set ,which is determined by the matrixM =[p 0 0 0 p 0 0 0 p]and the digit set D ={[0 0 0][1 1 0][0 1 1]},the spectrality and non-spectrality of the LZ（μM,D） is discussed.