| 李娜,李建林.有限uM,D-正交指数函数系的一个充分条件[J].数学年刊A辑,2019,40(4):457~466 |
| 有限uM,D-正交指数函数系的一个充分条件 |
| A Sufficient Condition for the Finite uM,D-Orthogonal Exponentials Function System |
| Received:July 14, 2015 Revised:December 29, 2015 |
| DOI：10.16205/j.cnki.cama.2019.0035 |
| 中文关键词: Self-affine measures, Orthogonal exponential function system, Non-spectrality, Determinant |
| 英文关键词:Self-affine measures, Orthogonal exponential function system, Non-spectrality, Determinant |
| 基金项目:本文受到国家自然科学基金(No.11171201,No.11571214)的资助. |
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| 中文摘要: |
| 设$\mu_{M,D}$是由仿射迭代函数系$\{\phi_{d}(x)=M^{-1}(x+d)\}_{d\in D}$唯一确定的自仿测度,
它的谱与非谱性质与Hilbert空间$L^{2}(\mu_{M,D})$中正交指数函数系的有限性和无限性有着直接的关系.
本文将利用矩阵的初等变换给出$\mu_{M,D}$\,{-}\!\!正交指数函数系有限性的一个充分条件. 由于这个条件只与
矩阵$M$的行列式有关, 因此, 它在$\mu_{M,D}$的非谱性的判断方面便于直接验证. |
| 英文摘要: |
| Let $\mu_{M,D}$ be a self-affine measure uniquely determined by the iterated function system
$\{\phi_{d}(x)=M^{-1}(x+d)\}_{d\in D}$.\ The spectrality or non-spectrality of $\mu_{M,D}$ is
directly connected with the finiteness or infiniteness of orthogonal exponentials in the Hilbert space
$L^{2}(\mu_{M,D})$. In this paper, the authors provide a sufficient condition for the finite
$\mu_{M,D}${-}orthogonal exponentials by applying the elementary matrix transformations.
This sufficient condition depends only upon the determinant of the matrix $M$,
and is easy to use in the research of non-spectrality of $\mu_{M,D}$. |
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