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Bounded remainder sets for rotations on the adelic torus


Authors: Joanna Furno, Alan Haynes and Henna Koivusalo
Journal: Proc. Amer. Math. Soc. 147 (2019), 5105-5115
MSC (2010): Primary 11J61, 11K38, 37A45
DOI: https://doi.org/10.1090/proc/14636
Published electronically: June 14, 2019
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Abstract: In this paper we give an explicit construction of bounded remainder sets of all possible volumes for any irrational rotation on the adelic torus $ \mathbb{A}/\mathbb{Q}$. Our construction involves ideas from dynamical systems and harmonic analysis on the adeles, as well as a geometric argument which originated in the study of deformation properties of mathematical quasicrystals.


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Additional Information

Joanna Furno
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: jfurno@math.uh.edu

Alan Haynes
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: haynes@math.uh.edu

Henna Koivusalo
Affiliation: Faculty of Mathematics, University of Vienna, A-1090 Vienna, Austria
Email: henna.koivusalo@univie.ac.at

DOI: https://doi.org/10.1090/proc/14636
Keywords: Bounded remainder sets, adeles, rotations on compact groups
Received by editor(s): October 17, 2018
Received by editor(s) in revised form: March 22, 2019
Published electronically: June 14, 2019
Additional Notes: Work of the third author was carried out on a visit to the University of Houston, supported by the Väisälä Fund.
Communicated by: Nimish Shah
Article copyright: © Copyright 2019 American Mathematical Society