NON-SPECTRALITY OF THE PLANAR SELF-AFFINE MEASURES WITH FOUR-ELEMENT DIGIT SETS
Keyword(s):
In this paper, we consider the non-spectrality of the planar self-affine measures [Formula: see text] generated by an expanding integer matrix [Formula: see text] and a four-element digit set [Formula: see text] We show that [Formula: see text] contains an infinite orthogonal set of exponential functions if and only if [Formula: see text]. Moreover, if [Formula: see text], then there exist at most [Formula: see text] mutually orthogonal exponential functions in [Formula: see text], and the number [Formula: see text] is the best.