- Title
- On a family of singular continuous measures related to the doubling map
- Creator
- Baake, Michael; Coons, Michael; Evans, James; Gohlke, Philipp
- Relation
- Indagationes Mathematicae Vol. 32, Issue 4, p. 847-860
- Publisher Link
- http://dx.doi.org/10.1016/j.indag.2021.06.001
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2021
- Description
- Here, we study some measures that can be represented by infinite Riesz products of 1-periodic functions and are related to the doubling map. We show that these measures are purely singular continuous with respect to Lebesgue measure and that their distribution functions satisfy super-polynomial asymptotics near the origin, thus providing a family of extremal examples of singular measures, including the Thue–Morse measure.
- Subject
- Riesz products; doubling map; singular continuous measures; hyperuniformity
- Identifier
- http://hdl.handle.net/1959.13/1491470
- Identifier
- uon:53042
- Identifier
- ISSN:0019-3577
- Language
- eng
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