00912nas a2200133 4500008004100000245004600041210004600087300001400133490000700147520053100154100001900685700002300704856005100727 2008 eng d00aUncertainty principles for compact groups0 aUncertainty principles for compact groups a1315-13240 v523 a
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.
1 aAlagic, Gorjan1 aRussell, Alexander uhttp://projecteuclid.org/euclid.ijm/1258554365