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This commit is contained in:
Stefan Kebekus 2024-05-15 15:31:57 +02:00
parent 4ff9c41ae3
commit 1c34aee7be
2 changed files with 10 additions and 3 deletions
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5
Nevanlinna/complexHarmonic.lean
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@ -254,11 +254,10 @@ theorem logabs_of_holomorphic_is_harmonic
rfl rfl
rw [this] rw [this]
have : ContDiff ℝ 2 (Complex.log ∘ f) := by sorry have : ContDiff ℝ 2 (Complex.log ∘ f) := by sorry
have : Complex.laplace (⇑Complex.imCLM ∘ f) = ⇑Complex.imCLM ∘ Complex.laplace (f) := by
apply laplace_compContLin
have : Complex.laplace (⇑Complex.conjCLE ∘ f) = ⇑Complex.conjCLE ∘ Complex.laplace (f) := by
sorry sorry
rw [laplace_compContLin this]
sorry sorry

8
Nevanlinna/laplace.lean
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@ -72,3 +72,11 @@ theorem laplace_compContLin {f : ℂ → F} {l : F →L[ℝ] G} (h : ContDiff
exact h.differentiable one_le_two exact h.differentiable one_le_two
exact (partialDeriv_contDiff ℝ h 1).differentiable le_rfl exact (partialDeriv_contDiff ℝ h 1).differentiable le_rfl
exact h.differentiable one_le_two exact h.differentiable one_le_two
theorem laplace_compCLE {f : ℂ → F} {l : F ≃L[ℝ] G} (h : ContDiff ℝ 2 f) :
Complex.laplace (l ∘ f) = l ∘ (Complex.laplace f) := by
let l' := (l : F →L[ℝ] G)
have : Complex.laplace (l' ∘ f) = l' ∘ (Complex.laplace f) := by
exact laplace_compContLin h
exact this