A class of spectral self-affine measures with four-element digit sets

The self-affine measure μM,DμM,D associated with an expanding matrix M∈Mn(Z)M∈Mn(Z) and a finite digit set D⊂ZnD⊂Zn is uniquely determined by the self-affine identity with equal weight. In this paper we construct a class of self-affine measures μM,DμM,D with four-element digit sets in the higher dimensions (n≥3n≥3) such that the Hilbert space L2(μM,D)L2(μM,D) possesses an orthogonal exponential basis. That is, μM,DμM,D is spectral. Such a spectral measure cannot be obtained from the condition of compatible pair. This extends the corresponding result in the plane.