| 有限uM,D-正交指数函数系的一个充分条件 |
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| 引用本文： | 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(中文版),2019,40(4):457-466. |
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| 作者姓名： | 李娜 李建林 |
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| 作者单位： | 陕西师范大学数学与信息科学学院, 陕西 西安 710119.,陕西师范大学数学与信息科学学院, 陕西 西安 710119. |
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| 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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| 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.
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| 关 键 词： | Self-affine measures Orthogonal exponential function system Non-spectrality Determinant |
| 收稿时间： | 2015/7/14 0:00:00 |
| 修稿时间： | 2015/12/29 0:00:00 |
A Sufficient Condition for the Finite uM,D-Orthogonal Exponentials Function System |
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| LI Na and LI Jianlin.A Sufficient Condition for the Finite uM,D-Orthogonal Exponentials Function System[J].Chinese Annals of Mathematics,2019,40(4):457-466. |
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| Authors: | LI Na and LI Jianlin |
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| Institution: | College of Mathematics and Information Science, Shaanxi Normal University, Xi''an 710119, Shaanxi, China. and College of Mathematics and Information Science, Shaanxi Normal University, Xi''an 710119, Shaanxi, China. |
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| Abstract: | 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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| Keywords: | Self-affine measures Orthogonal exponential function system Non-spectrality Determinant |
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