OAI/NumberTheory/Ostmann/Preliminaries/Autocorrelation.lean

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Additive autocorrelation

The probability-normalized Fourier transform of an autocorrelation is the squared modulus of the original transform. This is the positivity identity used for the bottom-pair coefficients in Section 6.

  1. def OAI.Ostmann.additiveConvolution line 17
  2. theorem OAI.Ostmann.additiveFourier_translation_sum line 21
  3. theorem OAI.Ostmann.additiveFourier_convolution line 36
  4. theorem OAI.Ostmann.additiveFourier_reflected_conj line 52
  5. def OAI.Ostmann.additiveAutocorrelation line 64
  6. theorem OAI.Ostmann.additiveAutocorrelation_eq_convolution line 68
  7. theorem OAI.Ostmann.additiveFourier_autocorrelation line 74