关于平面中一类特定数字集谱测度的探讨

摘要

讨论平面上由整数扩张矩阵M=[(ab)(dc)],det(M)=ac-bd∈2Z和数字集D={(00),(m0),(nk1),(lk2)}(m≠0,n,l∈Z,矗1,k2∈2Z+1)决定的L2 (μM,D)中无限正交系的存在性,及由M=((2b)(02)),b∈Z,D=(00),(10),(01),(k1k2))决定的μM,D是否是谱测度.%The existence of infinite orthogonal exponential functions for the space L2(μM,D) determined byrnthe integer expanding matrix M =[(ad) (bc)],det(M) = ac — bd ∈ 2Z and the digit set D =rn(00),(m0),(nk1),(lk2)}(m≠0,n,l∈Z+1) are discussed. In addition, whether or notrnμM,d is spectral measure determined by the matrix M = ((2b)(02)) ,b ∈ Z and the digit set D =rn{(00),(10),(01),(k1k2))}are discussed as well.