Theorems · Definition · functional analysis

SchwartzMap.smulLeftCLM

{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] → (E → 𝕜) → SchwartzMap E F →L[𝕜] SchwartzMap E F

The map f ↦ (x ↦ g x • f x) as a continuous 𝕜-linear map on Schwartz space, where g is a function of temperate growth.

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

41 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpace