Theorems · Theorem · functional analysis

SchwartzMap.smulLeftCLM_sum

∀ {ι : Type u_1} {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] {g : ι → E → 𝕜} {s : Finset ι},
  (∀ i ∈ s, Function.HasTemperateGrowth (g i)) →
    (SchwartzMap.smulLeftCLM F fun x => ∑ i ∈ s, g i x) = ∑ i ∈ s, SchwartzMap.smulLeftCLM F (g i)

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