OAI/MathematicalPhysics/DefocusingNLS/Linear/SchwartzPhysicalSampling.lean

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9 declarations, 0 contain sorry, 0 declared as axioms

The physical function of the uniformly bounded sampled vector

With the exact radian Fourier normalization, the sampled Y_L vector is the periodization of the original physical Schwartz function at period 2πL.

  1. def OAI.DefocusingNLS.periodizationRescale line 21
  2. theorem OAI.DefocusingNLS.periodizationRescale_apply line 25
  3. theorem OAI.DefocusingNLS.fourier_periodizationRescale line 29
  4. theorem OAI.DefocusingNLS.integerFourierCharacter_rescale line 51
  5. theorem OAI.DefocusingNLS.schwartz_physical_sampling_series line 62
  6. theorem OAI.DefocusingNLS.schwartzTorusSample_physical line 76
  7. theorem OAI.DefocusingNLS.one_le_norm_frequencyLattice line 87
  8. theorem OAI.DefocusingNLS.periodization_eq_of_support_ball line 102
  9. theorem OAI.DefocusingNLS.schwartzTorusSample_eq_on_ball line 119