An Uncertainty Inequality Involving L Norms

  title={An Uncertainty Inequality Involving L Norms},
  author={ENRICO LAENG and Carlo Morpurgo},
We derive a sharp uncertainty inequality of the form ‖xf‖1 ‖ξ f̂‖2 ≥ Λ0 4π2 ‖f‖1 ‖f‖2, with Λ0 = 0.428368 . . . . As a consequence of this inequality we derive an upper bound for the so-called Laue constant, that is, the infimum λ0 of the functional λ(p) = 4π‖xp‖1‖xp̂‖1/(p(0)p̂(0)), taken over all p ≥ 0 with p̂ ≥ 0 (p 6≡ 0). Precisely, we obtain that λ0 ≤ 2Λ0 = 0.85673673 . . . , which improves a previous bound of T. Gneiting. 

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