Theorems · Definition · functional analysis

TemperedDistribution.smulLeftCLM

{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] → (E → ℂ) → TemperedDistribution E F →L[ℂ] TemperedDistribution E F

Multiplication with a temperate growth function as a continuous linear map on 𝓢'(E, F).

Defined in

Mathlib.Analysis.Distribution.TemperedDistribution

Cited by

27 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul