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Update laplace.lean

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Stefan Kebekus
2024-05-13 09:52:15 +02:00
parent e5f2551482
commit 5e3f9c463f
1 changed files with 16 additions and 1 deletions
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Nevanlinna/laplace.lean
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@@ -15,6 +15,7 @@ import Nevanlinna.cauchyRiemann
import Nevanlinna.partialDeriv import Nevanlinna.partialDeriv
variable {F : Type*} [NormedAddCommGroup F] [NormedSpace ℝ F] variable {F : Type*} [NormedAddCommGroup F] [NormedSpace ℝ F]
variable {G : Type*} [NormedAddCommGroup G] [NormedSpace ℝ G]
noncomputable def Complex.laplace : (ℂ → F) → (ℂ → F) := noncomputable def Complex.laplace : (ℂ → F) → (ℂ → F) :=
@@ -43,7 +44,6 @@ theorem laplace_add {f₁ f₂ : ℂ → F} (h₁ : ContDiff ℝ 2 f₁) (h₂
exact h₂.differentiable one_le_two exact h₂.differentiable one_le_two
theorem laplace_smul {f : ℂ → F} (h : ContDiff ℝ 2 f) : ∀ v : ℝ, Complex.laplace (v • f) = v • (Complex.laplace f) := by theorem laplace_smul {f : ℂ → F} (h : ContDiff ℝ 2 f) : ∀ v : ℝ, Complex.laplace (v • f) = v • (Complex.laplace f) := by
intro v intro v
unfold Complex.laplace unfold Complex.laplace
@@ -57,3 +57,18 @@ theorem laplace_smul {f : ℂ → F} (h : ContDiff ℝ 2 f) : ∀ v : ℝ, Compl
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_compContLin {f : ℂ → F} {l : F →L[ℝ] G} (h : ContDiff ℝ 2 f) :
Complex.laplace (l ∘ f) = l ∘ (Complex.laplace f) := by
unfold Complex.laplace
rw [partialDeriv_compContLin]
rw [partialDeriv_compContLin]
rw [partialDeriv_compContLin]
rw [partialDeriv_compContLin]
simp
exact (partialDeriv_contDiff ℝ h Complex.I).differentiable le_rfl
exact h.differentiable one_le_two
exact (partialDeriv_contDiff ℝ h 1).differentiable le_rfl
exact h.differentiable one_le_two