Spectrality of self-affine measures and generalized compatible pairs
Spectrality of self-affine measures and generalized compatible pairs
复制标题
自仿射测度和广义兼容对的谱
DOI：
10.1007/s00605-017-1096-0
复制
发表时间：
2017-12-01
影响因子：
0.9
通讯作者：
Li, Jian-Lin
中科院分区：
文献类型：
--
作者：
Li, Jian-Lin
Let be a self-affine measure associated with an expanding matrix and a finite digit set . In this paper, we study the spectrality of by introducing the generalized compatible pairs via Hadamard matrices. This is motivated by the problem of looking for conditions for orthogonal exponential system to be infinite. Based on the properties of Hadamard matrices, we first present some elementary properties concerning the generalized compatible pair. We then provide a method of getting -orthogonal exponentials. Certain relationships between the generalized compatible pair and the spectrality of self-affine measure are established, which extend the known results in the appropriate manner. The research here is closely related to the spectral problem of self-affine measures.
