diff --git a/Nevanlinna/complexHarmonic.lean b/Nevanlinna/complexHarmonic.lean index 686ad1b..1f916e0 100644 --- a/Nevanlinna/complexHarmonic.lean +++ b/Nevanlinna/complexHarmonic.lean @@ -254,11 +254,10 @@ theorem logabs_of_holomorphic_is_harmonic rfl rw [this] 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 - rw [laplace_compContLin this] sorry diff --git a/Nevanlinna/laplace.lean b/Nevanlinna/laplace.lean index 2694a62..9d96a3c 100644 --- a/Nevanlinna/laplace.lean +++ b/Nevanlinna/laplace.lean @@ -72,3 +72,11 @@ theorem laplace_compContLin {f : ℂ → F} {l : F →L[ℝ] G} (h : ContDiff exact h.differentiable one_le_two exact (partialDeriv_contDiff ℝ h 1).differentiable le_rfl 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