Bohr sets in sumsets I: Compact abelian groups

Anh N. Le, Thái Hoà ng Lê

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