OAI/MathematicalPhysics/ContinuumCoulomb/OneParticle/GaussianMollification.lean

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Passing the proved Gaussian Poincare inequality to compact C¹ tests.

  1. theorem OAI.ContinuumCoulomb.gaussian_mollification_power_tendsto line 13
  2. theorem OAI.ContinuumCoulomb.gaussian_scalar_poincare line 35

    Source documentation

    The normalized Gaussian Poincare inequality on the exact C¹ test domain.

    theorem gaussian_scalar_poincare {freq : ℝ} (hf : 0 < freq)
    (f : ℝ → ℝ) (hs : ContDiff ℝ 1 f) (hc : HasCompactSupport f) :
    (2*freq)*((∫ z : ℝ, verticalMode freq z^2*f z^2) -
      (∫ z : ℝ, verticalMode freq z^2*f z)^2) ≤
        ∫ z : ℝ, verticalMode freq z^2*(deriv f z)^2 := by
…

    Mentions: OAI.ContinuumCoulomb.verticalMode