Abstract
Let [Formula: see text] be the unit matrix and [Formula: see text]. In this paper, we consider the self-similar measure [Formula: see text] on [Formula: see text] generated by the iterated function system [Formula: see text] where [Formula: see text]. We prove that there exists [Formula: see text] such that [Formula: see text] is an orthonormal basis for [Formula: see text] if and only if [Formula: see text] for some integer [Formula: see text].
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