Theorems · Theorem · functional analysis

SchwartzMap.fourierMultiplierCLM_apply

∀ {𝕜 : Type u_2} {E : Type u_3} {F : Type u_4} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace ℝ E] [inst_4 : NormedSpace ℂ F] [inst_5 : NormedSpace 𝕜 F]
  [inst_6 : SMulCommClass ℂ 𝕜 F] [inst_7 : FiniteDimensional ℝ E] [inst_8 : MeasurableSpace E] [inst_9 : BorelSpace E]
  (g : E → 𝕜) (f : SchwartzMap E F),
  (SchwartzMap.fourierMultiplierCLM F g) f =
    FourierTransformInv.fourierInv ((SchwartzMap.smulLeftCLM F g) (FourierTransform.fourier f))

Defined in

Mathlib.Analysis.Distribution.FourierMultiplier

Cited by

7 results in Mathlib

Foundations

Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedAddCommGroupInnerProductSpaceNormedSpaceNormedSpaceSMulCommClassFiniteDimensionalMeasurableSpaceBorelSpace