 For many cases of practical interest, the triple correlation of a function on an abstract group uniquely identifies that function up to a single unknown group action.This uniqueness is a mathematical result that relies on the Pontryagin duality theorem, the Tannaka–Krein duality theorem, and related results of Iwahori-Sugiura, and Tatsuuma.Algorithms exist for recovering bandlimited functions from their triple correlation on euclidean space, as well as rotation groups in two and three dimensions.