Small product sets in compact groups
Volume 238 / 2017
Fundamenta Mathematicae 238 (2017), 1-27
MSC: Primary 11P70; Secondary 22C05.
DOI: 10.4064/fm896-11-2016
Published online: 24 February 2017
Abstract
We show that a subcritical pair $(A,B)$ of sufficiently “spread-out” Borel sets in a compact and second countable group $K$ with an abelian identity component must reduce to a Sturmian pair in either $\mathbb {T}$ or $\mathbb {T}\rtimes \{-1,1\}$. This extends a classical result of Kneser.
