Local uncertainty inequalities for compact groups

Abstract

Conditions are established on α, β ∈ R for there to exist a constant K=K(α,β) such that Σ_γ∈Ed(γ)tr(f^{^}(γ)^∗f^{^}(γ))≤K(Σ_γ∈Ed(γ)²)^αIIω^βfII₂ for all f∈L¹(G) and E⊆G^{^} where G is a compact metric group, G^{^} is its dual, f^{^} is the Fourier transform of f and ω: G→R⁺ is the function taking x∈G to the area of the ball in G with centre e and x on its boundary. This is followed by a partial analogy for compact riemannian manifolds.