Spectrality of a class of moran measures on $\mathbb{R}^2$
Spectrality of a class of moran measures on $\mathbb{R}^2$
Let $\mu_{\{M_n\},\{D_n\}}$ be a Moran measure on $\mathbb{R}^2$ generated by a sequence of expanding matrices $\{M_n\}\subset GL(2, \mathbb{Z})$ and a sequence of integer digit sets $\{D_n\}$ where $D_n=\left\{\begin{pmatrix} 0 \\ 0 \end{pmatrix},\begin{pmatrix} \alpha_{n_1} \\ \alpha_{n_2} \end{pmatrix},\begin{pmatrix} \beta_{n_1} \\ \beta_{n_2} \end{pmatrix},\begin{pmatrix} -\alpha_{n_1}-\beta_{n_1} \\ -\alpha_{n_2}-\beta_{n_2} \end{pmatrix} \right\}$ with $\alpha_{n_1}\beta_{n_2}-\alpha_{n_2}\beta_{n_1}\notin2\mathbb{Z}$. If $|\det(M_n)|>4$ for …