一类直和数字集下正交指数函数系的基数

The Cardinality of Orthogonal Exponential Function Systems with a Class of Direct Sum Digital Sets

设M∈M2(■)为整数扩张矩阵,即M的所有特征值的模都大于1,D_1为有限数字集且D_1={(0 0),(-1 0),(11)},P=[0 p_1 p_2 0],其中p_1=±3,p_2=±1,当det(M)≠3■时,由整数扩张矩阵M和数字集D=D_1PD_1所确定的L^2(μ_(M,D))空间上正交指数函数系的基数为9,即μ_(M,D)为非谱测度.

Let MM2(■) be an expanding integer expansion matrix,that is,the modulus of all eigenvalues of M is greater than 1,D-1 is a finite digit set and D1={(0 0),(-1 0),(11)},P=[0 p1 p2 0],where p1=±3,p2=±1,when det(M)≠3■,the cardinal number of orthogonal exponential function system in L2(μM,D) space determined by integer expansion matrix M and digital set D = D1PD1 is 9,that is,μM,D is non-spectral measure.