Bohr sets in sumsets I: Compact abelian groups

Anh N. Le, Thái Hoàng Lê

Let $G$ be a compact abelian group and ${\varphi }_1,{\varphi }_2,{\varphi }_3$ be continuous endomorphisms on $G$. Under certain natural assumptions on the ${\varphi }_i$'s, we prove the existence of Bohr sets in…