The uncertainty principle and a generalization of a theorem of Tao

Let G be a finite abelian group. If f:G→C is a nonzero function with Fourier transform , the classical uncertainty principle states that . Recently, Tao showed that, if G is cyclic of prime order p, then in fact a stronger inequality holds. In this paper, we use representation theory of the unitary group and Weyl’s character formula to derive a generalization of Tao’s result for arbitrary finite cyclic groups.