Theorems · Theorem · functional analysis

SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv

∀ (𝕜 : Type u_2) {𝕜' : Type u_3} {D : Type u_4} {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : RCLike 𝕜]
  [inst_5 : NormedAddCommGroup D] [inst_6 : NormedSpace ℝ D] [inst_7 : NormedSpace 𝕜 F]
  [inst_8 : NontriviallyNormedField 𝕜'] [inst_9 : NormedAlgebra ℝ 𝕜'] [inst_10 : NormedSpace 𝕜' F] {u : D → 𝕜'},
  Function.HasTemperateGrowth u →
    ∀ (g : D ≃L[ℝ] E) (f : SchwartzMap E F),
      (SchwartzMap.smulLeftCLM F u) ((SchwartzMap.compCLMOfContinuousLinearEquiv 𝕜 g) f) =
        (SchwartzMap.compCLMOfContinuousLinearEquiv 𝕜 g) ((SchwartzMap.smulLeftCLM F (u ∘ ⇑g.symm)) f)

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceRCLikeNormedAddCommGroupNormedSpaceNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpace