Pontryagin duality
The Pontryagin dual of a locally compact abelian group, is the group formed by the continuous group homomorphisms from the group to the circle group. The Pontryagin duality theorem establishes Pontryagin duality by stating that any locally compact abelian group is naturally isomorphic with its bidual (the dual of its dual). Fourier inversion theorem is a special case of this theorem.