Abstract
In this paper, we study the spectral property of self-affine measures generated by an expanding integer matrix and a finite digit set , i.e. investigate whether the function in has a Fourier expansion. Let and for some integer . Through the discussion of the relationships between and , we establish some criteria to determine whether is spectral or non-spectral. Indeed, under those suitable assumptions, if is a spectral measure, we find its spectrum; otherwise, we give the maximum number of orthogonal exponential functions in . As an application, our results can contain some well-known conclusions.
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