Theorems · Theorem · functional analysis

SchwartzMap.smulLeftCLM_apply_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] {g : E → 𝕜},
  Function.HasTemperateGrowth g → ∀ (f : SchwartzMap E F) (x : E), ((SchwartzMap.smulLeftCLM F g) f) x = g x • f x

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

12 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpace