We establish an uncertainty principle over arbitrary compact groups, generalizing several previous results. Specifically, we show that if P and R are operators on L2(G) such that P commutes with projection onto every measurable subset of G and R commutes with left-multiplication by elements of G, then ∥PR∥≤∥P⋅χG∥2∥R∥2, where χG:g↦1 is the characteristic function of G. As a consequence, we show that every nonzero function f in L2(G) satisfies μ(suppf)⋅∑ρ∈G^dρrankf^(ρ)≥1.

VL - 52 U4 - 1315-1324 UR - http://projecteuclid.org/euclid.ijm/1258554365 CP - 4 U5 - doi:10.1215/ijm/1258554365 ER -