OAI/Analysis/ModularTheory/SpectralFourier.lean

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Fourier integration on compact spectral vectors. Compact support makes the character orbit norm-continuous in the bounded functional calculus, so integration can be transported through the actual calculus. This is the local bridge for the weighted Tomita calculation, not a trace assumption.

  1. lemma OAI.BoundedRecovery.spectralCharacter_pair line 17
  2. lemma OAI.BoundedRecovery.spectralFourierWeight_integrable line 26
  3. lemma OAI.BoundedRecovery.spectralFourierCutoff_integrable line 34
  4. def OAI.BoundedRecovery.spectralFourierCutoff line 46
  5. lemma OAI.BoundedRecovery.spectralFourierCutoff_apply line 50
  6. lemma OAI.BoundedRecovery.spectralGaussian_integrable line 66
  7. lemma OAI.BoundedRecovery.spectralGaussian_fourier line 70
  8. lemma OAI.BoundedRecovery.spectralFourierCutoff_gaussian line 86
  9. lemma OAI.BoundedRecovery.spectralFourierCutoff_calculus line 98