Compact Hankel operators on compact Abelian groups

The classical theorems of Kronecker, Hartman, Peller, and Adamyan–Arov–Krein are extended to the context of a connected compact Abelian group G G with linearly ordered group of characters, on the basis of a description of the structure of compact Hankel operators on G G . Beurling’s theorem on invariant subspaces is also generalized. Some applications to Hankel operators on discrete groups are given.