三元素数字集下L2(μM,D)上正交指数系的个数

摘要

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=((ab)(0c))(a,b,c∈Z,｜ a ｜＞1,｜ c ｜＞1,ac∈3Z)和数字集D={(00),(10),(10)}(l(￠){0,1})所决定的L2(μM,D)中正交指数函数的个数,以及对M =((p1m1m2)(0p2m3)(00p3)),M =((p0m)(0p0)(00p)),D ={(000),(100),(l00)}(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 deter-rnmined by the matrix M=((ab)(0c))(a,b,c∈Z,｜ a ｜＞1,｜ c ｜＞1,ac∈3Z) with D= {(00),(10),(10)}(l(￠){0,1}) and by the matrix M =((p1m1m2)(0p2m3)(00p3)),M =((p0m)(0p0)(00p)),D ={(000),(100),(l00)}(l(￠){0,1})rnP1tmltm2ttPt0tmrn0tP2tm3t, M =t0tpt0rn0t0tP3tt0t0tprnwith D=rn0tt1tt1rn0t,t0t,t0rn0tt0tt0rn, are discussed. And the best estimation can be found.