OAI/MathematicalPhysics/DefocusingNLS/Linear/HomogeneousCommutatorBound.lean

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7 declarations, 0 contain sorry, 0 declared as axioms

The high-frequency gain for the physical derivative commutator

For a Schwartz input with frequencies above R, the actual commutator costs only R⁻¹ times its top homogeneous energy. The coefficient is an explicit integrable Fourier moment of the fixed Schwartz potential.

  1. theorem OAI.DefocusingNLS.two_add_pow_le line 19
  2. def OAI.DefocusingNLS.homogeneousCommutatorMoment line 31
  3. theorem OAI.DefocusingNLS.homogeneousCommutatorMoment_nonneg line 34
  4. theorem OAI.DefocusingNLS.homogeneousCommutatorMoment_integrable line 39
  5. theorem OAI.DefocusingNLS.commutator_integrand_high line 49
  6. theorem OAI.DefocusingNLS.homogeneousOrderedCommutator_high_pointwise line 89
  7. theorem OAI.DefocusingNLS.homogeneousOrderedCommutator_high_energy line 126