Theorems · Theorem · functional analysis

SchwartzMap.smulLeftCLM_smulLeftCLM_apply

∀ {𝕜 : Type u_2} {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 : NontriviallyNormedField 𝕜]
  [inst_5 : NormedAlgebra ℝ 𝕜] [inst_6 : NormedSpace 𝕜 F] {g₁ g₂ : E → 𝕜},
  Function.HasTemperateGrowth g₁ →
    Function.HasTemperateGrowth g₂ →
      ∀ (f : SchwartzMap E F),
        (SchwartzMap.smulLeftCLM F g₁) ((SchwartzMap.smulLeftCLM F g₂) f) = (SchwartzMap.smulLeftCLM F (g₁ * g₂)) f

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

3 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpace