Cocycles and Local Product Decomposition

Abstract

As an application of cocycles, we establish a relation between the classical Hardy spaces on the real line $R$ and simply invariant subspaces on a quotient of the Bohr group. When this result is specialized suitably, it yields the well-known results concerning the elements of invariant subspaces. We also study, by using Gamelin’s representation theorem, unitary functions which are the values of cocycles.