Theorems · Theorem · functional analysis

ContDiffMapSupportedIn.seminorm_postcompLM_le

∀ (𝕜 : Type u_1) {E : Type u_2} {F : Type u_3} {F' : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F]
  [inst_5 : NormedSpace 𝕜 F] [inst_6 : SMulCommClass ℝ 𝕜 F] [inst_7 : NormedAddCommGroup F'] [inst_8 : NormedSpace ℝ F']
  [inst_9 : NormedSpace 𝕜 F'] [inst_10 : SMulCommClass ℝ 𝕜 F'] {n : ℕ∞} {K : TopologicalSpace.Compacts E}
  [inst_11 : LinearMap.CompatibleSMul F F' ℝ 𝕜] {i : ℕ} (T : F →L[𝕜] F') (f : ContDiffMapSupportedIn E F n K),
  (ContDiffMapSupportedIn.seminorm 𝕜 E F' n K i) ((ContDiffMapSupportedIn.postcompLM T) f) ≤
    ‖T‖ * (ContDiffMapSupportedIn.seminorm 𝕜 E F n K i) f

Defined in

Mathlib.Analysis.Distribution.ContDiffMapSupportedIn

Cited by

0 results in Mathlib

Foundations

Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedSpaceSMulCommClassNormedAddCommGroupNormedSpaceNormedSpaceSMulCommClassLinearMap.CompatibleSMul