Bounded Solutions of n-Cocycle And Related Equations on Amenable Semigroups

The cocycle functional equation, originating in group theory and playing a role in such areas as cohomology, polyhedral algebra, and information theory, has a long and rich history. Cocycles of higher orders have been introduced in cohomology theory. This paper presents the bounded solutions of cocycle equations of all orders on amenable semigroups. Some related functional equations are treated also. These results generalize some recent results of Pales and Szekelyhidi.