Orthogonal exponentials of self-affine measures on ℝn
Keyword(s):
The Self
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Let the self-affine measure [Formula: see text] be generated by an expanding matrix [Formula: see text] and a finite integer digit set [Formula: see text], where [Formula: see text] with [Formula: see text] and [Formula: see text]. In this paper, we show that if [Formula: see text] for an integer [Formula: see text], then [Formula: see text] admits an infinite orthogonal set of exponential functions if and only if there exists [Formula: see text] such that [Formula: see text] for some [Formula: see text] with [Formula: see text] and [Formula: see text].