Let G be a finite nonabelian group. Bent functions on G are defined by the Fourier transforms at irreducible representations of G. We introduce a dual basis G^ , consisting of functions on G determined by its unitary irreducible representations, that will play a role similar to the dual group of a finite abelian group. Then we define the Fourier transforms as functions on G^ , and obtain characterizations of a bent function by its Fourier transforms (as functions on G^). For a function f from G to another finite group, we define a dual function...
