OAI/MathematicalPhysics/DefocusingNLS/Linear/SchwartzPoissonSummation.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

Poisson summation for the actual twelve-dimensional Fourier lattice

The periodic function is the locally normally convergent sum of Schwartz translates. Computing its Fourier coefficients on a fundamental cell and using the existing multivariate Fourier basis identifies its Fourier series.

  1. theorem OAI.DefocusingNLS.unitTorus_integral_eq_frequencyCell line 23
  2. def OAI.DefocusingNLS.integerFourierCharacter line 50
  3. theorem OAI.DefocusingNLS.integerFourierCharacter_norm line 54
  4. theorem OAI.DefocusingNLS.unitTorusProjection_add_lattice line 59
  5. theorem OAI.DefocusingNLS.integerFourierCharacter_periodic line 68
  6. theorem OAI.DefocusingNLS.integerFourierCharacter_exp line 74
  7. theorem OAI.DefocusingNLS.schwartzPeriodizedTorus_fourierCoeff line 89
  8. theorem OAI.DefocusingNLS.schwartz_poisson_summation line 110