Uncertainty Principles for Compact Groups

We establish an operator-theoretic uncertainty principle over arbitrary compact groups, generalizing several previous results. As a consequence, we show that every nonzero square-integrable function f on a compact group G satisfies μ(supp f) · P ρ∈Ĝ dρ rk f̂(ρ) ≥ 1. For finite groups, our principle implies the following: if P and R are projection operators on the group algebra CG such that P commutes with projection onto each group element, and R commutes with left multiplication, then ‖PR ‖ ≤ (rkP rkR)/|G|.