Theorems · Theorem · integral transforms

HasCompactSupport.contDiff_convolution_right

∀ {𝕜 : Type u𝕜} {G : Type uG} {E : Type uE} {E' : Type uE'} {F : Type uF} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup E'] [inst_2 : NormedAddCommGroup F] {f : G → E} {g : G → E'} [inst_3 : RCLike 𝕜]
  [inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜 E'] [inst_6 : NormedSpace ℝ F] [inst_7 : NormedSpace 𝕜 F]
  [inst_8 : MeasurableSpace G] [inst_9 : NormedAddCommGroup G] [BorelSpace G] [inst_11 : NormedSpace 𝕜 G]
  {μ : MeasureTheory.Measure G} (L : E →L[𝕜] E' →L[𝕜] F) {n : ℕ∞},
  HasCompactSupport g →
    MeasureTheory.LocallyIntegrable f μ → ContDiff 𝕜 (↑n) g → ContDiff 𝕜 (↑n) (MeasureTheory.convolution f g L μ)

Defined in

Mathlib.Analysis.Calculus.ContDiff.Convolution

Cited by

1 results in Mathlib

Foundations

Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNormedAddCommGroupRCLikeNormedSpaceNormedSpaceNormedSpaceNormedSpaceMeasurableSpaceNormedAddCommGroupBorelSpaceNormedSpace