Eigenfunctions for Substitution Tiling Systems
نویسنده
چکیده
We prove that for the uniquely ergodic R action associated with a primitive substitution tiling of finite local complexity, every measurable eigenfunction coincides with a continuous function almost everywhere. Thus, topological weak-mixing is equivalent to measure-theoretic weak-mixing for such actions. If the expansion map for the substitution is a pure dilation by θ > 1 and the substitution has a fixed point, then failure of weak-mixing is equivalent to θ being a Pisot number.
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تاریخ انتشار 2007