Abstract
Let be a self-affine measure associated with an expanding matrix and a finite digit set . We consider in this paper the spectrality of . In the case when is a compatible pair for some , a necessary condition is obtained for the spectral pair . This condition is shown to be equivalent to the known necessary conditions for the same spectral pair. Moreover, we prove that all these necessary conditions are not sufficient in the higher dimensions, but they are sufficient in the dimension one. This extends Laba-Wang's condition for spectral pairs.
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