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Update complexHarmonic.lean

This commit is contained in:
Stefan Kebekus 2024-05-02 17:55:26 +02:00
parent b9a973d10d
commit f239759275
1 changed files with 1 additions and 13 deletions
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Nevanlinna/complexHarmonic.lean
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@ -17,18 +17,6 @@ noncomputable def Complex.laplace : (ℂ → ℝ) → (ℂ → ℝ) := by
def Harmonic (f : ℂ → ℝ) : Prop := def Harmonic (f : ℂ → ℝ) : Prop :=
(ContDiff ℝ 2 f) ∧ (∀ z, Complex.laplace f z = 0) (ContDiff ℝ 2 f) ∧ (∀ z, Complex.laplace f z = 0)
#check contDiff_iff_ftaylorSeries.2
lemma c2_if_holomorphic (f : ℂ → ℂ) : Differentiable ℂ f → ContDiff ℂ 2 f := by
intro fHyp
exact Differentiable.contDiff fHyp
lemma c2R_if_holomorphic (f : ℂ → ℂ) : Differentiable ℂ f → ContDiff ℝ 2 f := by
intro fHyp
let ZZ := c2_if_holomorphic f fHyp
apply ContDiff.restrict_scalars ℝ ZZ
theorem re_comp_holomorphic_is_harmonic (f : ℂ → ℂ) : theorem re_comp_holomorphic_is_harmonic (f : ℂ → ℂ) :
Differentiable ℂ f → Harmonic (Complex.reCLM ∘ f) := by Differentiable ℂ f → Harmonic (Complex.reCLM ∘ f) := by
@ -41,7 +29,7 @@ theorem re_comp_holomorphic_is_harmonic (f : ℂ → ℂ) :
· -- Complex.reCLM is two times real continuously differentiable · -- Complex.reCLM is two times real continuously differentiable
exact ContinuousLinearMap.contDiff Complex.reCLM exact ContinuousLinearMap.contDiff Complex.reCLM
· -- f is two times real continuously differentiable · -- f is two times real continuously differentiable
exact c2R_if_holomorphic f h exact ContDiff.restrict_scalars ℝ (Differentiable.contDiff h)
· -- Laplace of f is zero · -- Laplace of f is zero
intro z intro z