Pisot family self-affine tilings, discrete spectrum, and the Meyer property
Pisot family self-affine tilings, discrete spectrum, and the Meyer property
We consider self-affine tilings in the Euclidean space and theassociated tiling dynamical systems, namely, the translationaction on the orbit closure of the given tiling. We investigatethe spectral properties of the system. It turns out that thepresence of the discrete component depends on the algebraicproperties of the eigenvalues of the expansion …