Abstract
For the self-affine measure [Formula: see text] generated by an expanding matrix [Formula: see text] and an integer digit set [Formula: see text] with [Formula: see text], Su et al. proved that if [Formula: see text], then [Formula: see text] contains an infinite orthogonal set of exponential functions if and only if [Formula: see text] [J. Su, Y. Liu and J. C. Liu, Non-spectrality of the planar self-affine measures with four-element digit sets, Fractals (2019), https://doi.org/10.1142/S0218348X19501159 ]. In this paper, we show that the above conclusion also holds for [Formula: see text]. So, a complete characterization of [Formula: see text] containing an infinite orthogonal set of exponential functions is given.
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