diff --git a/Nevanlinna/diffOp.lean b/Nevanlinna/diffOp.lean index 5260e55..1d25981 100644 --- a/Nevanlinna/diffOp.lean +++ b/Nevanlinna/diffOp.lean @@ -5,7 +5,7 @@ import Mathlib.Analysis.InnerProductSpace.PiL2 Let E, F, G be vector spaces over nontrivally normed field 𝕜, a homogeneus linear differential operator of order n is a map that attaches to every point e -of E a linear evaluation +of E a linear evaluation {Continuous 𝕜-multilinear maps E → F in n variables} → G @@ -22,7 +22,7 @@ fun e ↦ D e (iteratedFDeriv 𝕜 n f e) -/ @[ext] -class HomLinDiffOp +class HomLinDiffOp (𝕜 : Type*) [NontriviallyNormedField 𝕜] (n : ℕ) (E : Type*) [NormedAddCommGroup E] [NormedSpace 𝕜 E] @@ -59,13 +59,13 @@ noncomputable def Laplace exact { toFun := fun f' ↦ ∑ i, f' ![v i, v i] - map_add' := by + map_add' := by intro f₁ f₂ - exact Finset.sum_add_distrib + exact Finset.sum_add_distrib map_smul' := by intro m f exact Eq.symm (Finset.mul_sum Finset.univ (fun i ↦ f ![v i, v i]) m) - cont := by + cont := by simp apply continuous_finset_sum intro i _ @@ -86,13 +86,13 @@ noncomputable def Gradient exact { toFun := fun f' ↦ ∑ i, (f' ![v i]) • (v i) - map_add' := by + map_add' := by intro f₁ f₂ simp; simp_rw [add_smul, Finset.sum_add_distrib] map_smul' := by intro m f simp; simp_rw [Finset.smul_sum, ←smul_assoc,smul_eq_mul] - cont := by + cont := by simp apply continuous_finset_sum intro i _