The appropriate choice of scaling to achieve unitarity is , so that the energy in the physical domain will be the same as the energy in the Fourier domain, i.e., to satisfy Parseval's theorem.
Quentin de Parseval (born 1987), defender currently playing for French Championnat National club SC
More generally, given an abelian topological group G with Pontryagin dual G^, Parseval's theorem says the Pontryagin–Fourier transform is a unitary operator between Hilbert spaces L2(G) and L2(G^) (with integration being against the appropriately scaled Haar measures on the two groups.) When G is the unit circle T, G^ is the integers and this is the case discussed above.
Quentin de Parseval | Parseval's theorem | Parseval | August von Parseval |
After tests of the different available airship types, the semi-rigid Groß airship and the Parseval blimp were abandoned while the rigid airships of Zeppelin and Schütte-Lanz design were selected for service.