OAI/Geometry/SurfaceImmersion/Correction/SmoothingConvolution.lean

GitHub source file

11 declarations, 0 contain sorry, 0 declared as axioms

The actual smoothing operators from the finite-moment kernels. They are linear on locally integrable inputs, smooth their outputs, and fix constants.

  1. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.kernel line 15
  2. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.kernel_smooth line 17
  3. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.kernel_compact line 20
  4. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.kernel_mass line 23
  5. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.kernel_moment line 26
  6. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.mass_dilate line 30
  7. def OAI.ClosedSurfaceR4.FiniteOrderSmoothing.smooth line 38

    Source documentation

    Smoothing at scale s, using the kernel whose moments vanish through r.

    def smooth (r : ℕ) (s : ℝ) (f : Base → E) : Base → E :=
…
  8. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.smooth_smooth line 42
  9. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.smooth_add line 48
  10. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.smooth_smul line 57
  11. lemma OAI.ClosedSurfaceR4.FiniteOrderSmoothing.smooth_const line 61