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.
The uniqueness is a mathematical outcome derived from the Pontryagin duality theorem, the Tannaka–Krein duality theorem, and related results by Iwahori-Sugiura and Tatsuuma. Algorithms exist to reconstruct bandlimited functions using their triple correlation in Euclidean space and for rotation groups in two and three dimensions.