Uniformity of spectral self-affine measures

Uniformity of spectral self-affine measures

For an arbitrary self-affine measure defined by a self-affine iterated function system and a family of probability weights, it is proven in this article that, if a self-affine measure is a spectral measure, then the probability weights must be equal and measure non-overlap holds in a weaker sense. I...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2021-03, Vol.380, p.107568, Article 107568
Hauptverfasser: Deng, Qi-Rong, Chen, Jian-Bao
Format: Artikel
Sprache:eng
Schlagworte:
Equal probability weights
Measure non-overlap
Self-affine
Spectral measure
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Zusammenfassung:For an arbitrary self-affine measure defined by a self-affine iterated function system and a family of probability weights, it is proven in this article that, if a self-affine measure is a spectral measure, then the probability weights must be equal and measure non-overlap holds in a weaker sense. In particular, all spectral integral self-affine measures satisfy the OSC.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2021.107568