三元素数字集下L^2_((μM,D))上正交指数系的个数

The cardinality of orthogonal exponential on the L^2_((μM,D)) with three-element digit set

自仿测度μM,D是由{φd(x)=M-1(x+d)}d∈D惟一确定的.借助模3的剩余类,讨论矩阵M=ab0c(a,b,c∈Z,|a|>1,|c|>1,ac∈3Z)和数字集D=((00),(10),l0}(l{0,1})所决定的L2(μM,D)中正交指数函数的个数,以及对M=p1 m1m20 p2m30 0 p3,M=p 0 m 0 p 0 0 0 p,D={{000},{100},{100}}l{0,1}),所决定的L2(μM,D)中正交指数函数的个数,并找出最好的估计.

The self-affine measures μM,D is decided by {φd（x）=M-1（x＋d） }d∈D.By use of the residue class of three,the number of the orthogonal exponential functions for the L2（μM,D） space which is determined by the matrix M=p1 m1m20 p2m30 0 p3,M=p 0 m 0 p 0 0 0 p,D={{000},{100},{100}}l{0,1}）,and by the matrix M=,M= with D=,,are discussed.And the best estimation can be found.