Let
$$\mu _{M,D}$$
be the self-affine measure associated with an expanding integer matrix
$$M=\left( \begin{array}{cc} p &{} 0 \\ 0 &{} q \\ \end{array}\right) $$
and
$$D=\left\{ \,\,\begin{pmatrix} 0\\ 0 \end{pmatrix},\,\,\,\begin{pmatrix} 1\\ 1 \end{pmatrix} \,\,\right\} $$
, where |p| and |q| are distinct odd bigger than 1. Such a measure is the simplest and the most important case in the study of the spectral property of self-affine measures with two-elements digit sets, which is an open problem up to now. In this paper, we first construct two classes of 4-...
