Uncertainty principles for compact groups
Gorjan Alagic and Alexander Russell
Source: Illinois J. Math. Volume 52, Number 4
(2008), 1315-1324.
Abstract
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(supp f) ⋅ ∑ρ∈Ĝdρrank ̂f(ρ)≥1.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ijm/1258554365
Zentralblatt MATH identifier: 05660661
Mathematical Reviews number (MathSciNet): MR2595770
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