Spectral property of self-affine measures on

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• 作者：Jing-Cheng Liu^a ; ^{liujingcheng11@126.com" class="auth_mail" title="E-mail the corresponding author} ; Jun Jason Luo^b ; ^{jun.luo@cqu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 42C05 ; secondary ; 28A80
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：272
• 期：2
• 页码：599-612
• 全文大小：347 K

文摘

We study spectral properties of the self-affine measure bebf5a29745f" title="Click to view the MathML source">μ_M,D${\mu }_{M,\mathcal{D}}$ generated by an expanding integer matrix M∈M_n(Z)$M\in M_n(\mathbb{Z})$ and a consecutive collinear digit set D={0,1,…,q−1}v$\mathcal{D}=\{0,1,\dots ,q-1\}v$ where v∈Zⁿ∖{0}$v\in {\mathbb{Z}}^n\setminus \{0\}$ and q≥2$q\ge 2$ is an integer. Some sufficient conditions for bebf5a29745f" title="Click to view the MathML source">μ_M,D${\mu }_{M,\mathcal{D}}$ to be a spectral measure or to have infinitely many orthogonal exponentials are given. Moreover, for some special cases, we can obtain a necessary and sufficient condition on the spectrality of bebf5a29745f" title="Click to view the MathML source">μ_M,D${\mu }_{M,\mathcal{D}}$. Our study generalizes the one dimensional results proved by Dai, et al.  and .