Title | Uncertainty principles for compact groups |

Publication Type | Journal Article |

Year of Publication | 2008 |

Authors | Alagic, G, Russell, A |

Journal | Illinois J. Math. |

Volume | 52 |

Issue | 4 |

Pages | 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(suppf)⋅∑ρ∈G^dρrankf^(ρ)≥1. |

URL | http://projecteuclid.org/euclid.ijm/1258554365 |

DOI | 10.1215/ijm/1258554365 |