L^2空间中的非谱问题

Non-spectral problem in L^2-spaces

证明了与扩张矩阵M∈Mn(R),有限子集D Rn相关的自仿测度μM,D是由迭代函数系{φd(x)=M-1(x+d)}d∈D所惟一确定的,其中μM,D的非谱问题之一就是估计L2(μM,D)空间中指数正交系的个数并且找到它们.讨论了如果pi∈2Z+1,|pi|>1(i=1,2,3),p1 3,M=(p10 00p200 0p3),D=(000,100,l00)(l∈3Z+2,且l{0,1}),那么L2(μM,D)中至多存在3个指数正交系,而且数字3是最好的.

The self-aft＇me measure μM,D corresponding to an expanding matrix M∈Mn（R） and a finite subset D Rn is uniquely determined by the iterated function system One of the non-spectral problem on μM,D is to estimate the number of orthogonal exponentials in L2 （μM,D ） and to find them. It is proved that if , then there are at most 3 mutually orthogonal exponentials inLz （μM,D ） , and the number 3 is the best.