OAI/MathematicalPhysics/DefocusingNLS/Linear/ExpandingEnergyComponents.lean

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10 declarations, 0 contain sorry, 0 declared as axioms

The two exact energy components on an expanding torus

The normalized Fourier space has a fixed Hilbert norm. These two bounded observations recover the low and high terms of the radius-dependent norm.

  1. def OAI.DefocusingNLS.expandingLowFraction line 15
  2. theorem OAI.DefocusingNLS.expandingLowFraction_bounds line 18
  3. theorem OAI.DefocusingNLS.expandingHighFraction_eq line 27
  4. def OAI.DefocusingNLS.fourierEnergyComponent line 37
  5. theorem OAI.DefocusingNLS.fourierEnergyComponent_apply line 60
  6. theorem OAI.DefocusingNLS.fourierEnergyComponent_norm_sq line 64
  7. theorem OAI.DefocusingNLS.summable_fourierEnergyComponent line 76
  8. def OAI.DefocusingNLS.expandingLowEnergy line 86
  9. def OAI.DefocusingNLS.expandingHighEnergy line 90
  10. theorem OAI.DefocusingNLS.expandingEnergy_norm_sq line 96