OAI/Analysis/KadisonKastler/ThresholdCutIntegral.lean

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Averaging finite spectral threshold cuts

Two spectral values are separated by a threshold on an interval of length equal to their distance. Finite weighted sums give the exact average cut energy and its Cauchy--Schwarz bound.

  1. def OAI.KadisonKastler.thresholdDifference line 21
  2. theorem OAI.KadisonKastler.thresholdDifference_sq line 24
  3. theorem OAI.KadisonKastler.thresholdDifference_sq_integrable line 44
  4. theorem OAI.KadisonKastler.integral_thresholdDifference_sq line 50
  5. theorem OAI.KadisonKastler.integral_weighted_thresholdDifference_sq line 58
  6. theorem OAI.KadisonKastler.weighted_threshold_energy_le line 67