Theorems · Theorem · functional analysis

ContDiffMapSupportedIn.bilinLeftCLM_apply

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace ℝ E] {n : ℕ∞} {K : TopologicalSpace.Compacts E} {F₁ : Type u_5} {F₂ : Type u_6} {F₃ : Type u_7}
  [inst_3 : NormedAlgebra ℝ 𝕜] [inst_4 : NormedAddCommGroup F₁] [inst_5 : NormedSpace 𝕜 F₁] [inst_6 : NormedSpace ℝ F₁]
  [inst_7 : NormedAddCommGroup F₂] [inst_8 : NormedSpace 𝕜 F₂] [inst_9 : NormedSpace ℝ F₂]
  [inst_10 : NormedAddCommGroup F₃] [inst_11 : NormedSpace 𝕜 F₃] [inst_12 : NormedSpace ℝ F₃] (B : F₁ →L[𝕜] F₂ →L[𝕜] F₃)
  {g : E → F₂} (hg : ContDiff ℝ (↑n) g) (φ : ContDiffMapSupportedIn E F₁ n K),
  ⇑((ContDiffMapSupportedIn.bilinLeftCLM B hg) φ) = fun x => (B (φ x)) (g x)

Defined in

Mathlib.Analysis.Distribution.ContDiffMapSupportedIn

Cited by

0 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAlgebraNormedAddCommGroupNormedSpaceNormedSpaceNormedAddCommGroupNormedSpaceNormedSpaceNormedAddCommGroupNormedSpaceNormedSpace