关于L^2(μ_(M,D))上指数正交系个数的讨论

The number of orthogonal exponentials on the L^2(μ_(M,D))-space

自仿测度μM,D是由{d(x)=M-1(x+d)}d∈D惟一确定的.对于扩张矩阵M∈Mn(Z)即M=[ad bc],D={(00),(10),(20),(11)},且ac-bd∈2Z,通过讨论其自仿测度的Fourier变换零点的性质,得出这个特殊的L2(μM,D)空间上的指数正交系的个数.

The self-affine measures is decided by{d（x）=M-1（x＋d）}d∈ D.When M∈Mn（Z）,M=[ad bc],D={（00）,（10）,（20）,（11）},and ac-bd∈2Z,by discussing the properties of the zero points of the self-affine measure＇s fourier transform,the number of orthogonal exponentials in a special L2（μM,D） space is obtained.