  We consider compact and connected Abelian group $G$ with a linearly ordered
dual. Based on the description of the structure of compact Hankel operators
over $G$, generalizations of the classical Kronecker, Hartman, Peller and
Adamyan-Arov-Krein theorems are obtained. A generalization of Burling's
invariant subspace theorem is also established. Applications are given to
Hankel operators over discrete groups
