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159357f | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 | import Mathlib
import OAI.Analysis.CoulombIonization.FormDomain.L2
namespace OAI
noncomputable section
open MeasureTheory Filter
open scoped Topology BigOperators ContDiff
open MeasureTheory Filter Complex TopologicalSpace
open scoped Topology InnerProductSpace ENNReal
open MeasureTheory Filter Complex
open scoped Topology BigOperators ComplexConjugate FourierTransform SchwartzMap ENNReal
open MeasureTheory Filter
open scoped Topology ContDiff SchwartzMap FourierTransform ENNReal
open MeasureTheory Filter
open scoped ContDiff InnerProductSpace Topology
open MeasureTheory Filter
open scoped ENNReal
namespace CoulombSobolev.Test
variable {E F : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
[NormedAddCommGroup F] [NormedSpace ℝ F]
def compCL (φ : Test F) (e : E ≃L[ℝ] F) : Test E where
fn x := φ.fn (e x)
smooth := φ.smooth.comp e.contDiff
compact := φ.compact.comp_homeomorph e.toHomeomorph
lemma ext_fn {φ η : Test E} (h : φ.fn = η.fn) : φ = η := by
cases φ; cases η; cases h; rfl
lemma compCL_deriv (φ : Test F) (e : E ≃L[ℝ] F) (v : E) :
(φ.compCL e).deriv v = (φ.deriv (e v)).compCL e := by
apply ext_fn
funext x
change fderiv ℝ (φ.fn ∘ e) x v = _
rw [fderiv_comp x (φ.smooth.differentiable (by simp) _) e.differentiableAt]
simp only [ContinuousLinearEquiv.fderiv, ContinuousLinearMap.comp_apply]
rfl
end CoulombSobolev.Test
end
end OAI
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