OAI/Analysis/LipschitzHilbert/Fourier/SmoothSlopeSymbol.lean

GitHub source file

14 declarations, 0 contain sorry, 0 declared as axioms

A smooth extension of the slope denominator gives the full normalized symbol, including its slope partition and vertical frequency window.

  1. def OAI.LipschitzHilbert.PacketRepresentation.positiveDenominator line 12
  2. theorem OAI.LipschitzHilbert.PacketRepresentation.positiveDenominator_lower line 15
  3. theorem OAI.LipschitzHilbert.PacketRepresentation.positiveDenominator_eq line 24
  4. theorem OAI.LipschitzHilbert.PacketRepresentation.positiveDenominator_contDiff line 31
  5. def OAI.LipschitzHilbert.PacketRepresentation.masterVertical line 35
  6. theorem OAI.LipschitzHilbert.PacketRepresentation.masterVertical_contDiff line 37
  7. def OAI.LipschitzHilbert.PacketRepresentation.masterSlopeArgument line 41
  8. theorem OAI.LipschitzHilbert.PacketRepresentation.masterSlopeArgument_contDiff line 44
  9. theorem OAI.LipschitzHilbert.PacketRepresentation.masterCutoff_hasCompactSupport line 50
  10. def OAI.LipschitzHilbert.PacketRepresentation.partitionedMasterSymbol line 55
  11. theorem OAI.LipschitzHilbert.PacketRepresentation.partitionedMasterSymbol_apply line 64
  12. def OAI.LipschitzHilbert.PacketRepresentation.partitionedSymbol line 69
  13. theorem OAI.LipschitzHilbert.PacketRepresentation.partitionedSymbol_apply line 73
  14. theorem OAI.LipschitzHilbert.PacketRepresentation.partitionedSymbol_uniform line 84