Theorems · Theorem · functional analysis

TemperedDistribution.smulLeftCLM_apply_apply

∀ {E : Type u_3} {F : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : AddCommGroup F]
  [inst_3 : Module ℂ F] [inst_4 : TopologicalSpace F] [inst_5 : IsTopologicalAddGroup F]
  [inst_6 : ContinuousConstSMul ℂ F] (g : E → ℂ) (f : TemperedDistribution E F) (f' : SchwartzMap E ℂ),
  ((TemperedDistribution.smulLeftCLM F g) f) f' = f ((SchwartzMap.smulLeftCLM ℂ g) f')

Defined in

Mathlib.Analysis.Distribution.TemperedDistribution

Cited by

12 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul