Controllability, observability, and duality in behavioral group systems

Fundamental results concerning abelian group systems and their duals are developed. Duals of sequence spaces over locally compact abelian groups are defined via Pontryagin duality; dual group systems are orthogonal subgroups of dual sequence spaces. If C and C^⊥ are dual systems then the state spaces of C are isomorphic to the character groups of the state spaces of C^⊥. Further, the controllability properties of C are equal to the observability properties of C^⊥