Theorems · Theorem · functional analysis

TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq

∀ {E : Type u_3} {F : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
  [inst_2 : InnerProductSpace ℝ E] [inst_3 : NormedSpace ℂ F] [inst_4 : FiniteDimensional ℝ E]
  [inst_5 : MeasurableSpace E] [inst_6 : BorelSpace E] [CompleteSpace F] {g : E → ℂ},
  Function.HasTemperateGrowth g →
    ∀ (f : SchwartzMap E F),
      (TemperedDistribution.fourierMultiplierCLM F g)
          ((SchwartzMap.toTemperedDistributionCLM E F MeasureTheory.volume) f) =
        (SchwartzMap.toTemperedDistributionCLM E F MeasureTheory.volume) ((SchwartzMap.fourierMultiplierCLM F g) f)

Defined in: Mathlib.Analysis.Distribution.FourierMultiplier
Cited by: 1 results in Mathlib
Foundations: Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedAddCommGroup InnerProductSpace NormedSpace FiniteDimensional MeasurableSpace BorelSpace CompleteSpace

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DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
RingHom.idstatement and proof · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
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Set.Elemstatement · cited by 7,166
Set.ofPredstatement · cited by 6,101
Complexstatement and proof · cited by 5,565
ContinuousLinearMapstatement · cited by 5,352
InnerProductSpacestatement and proof · cited by 3,523

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SchwartzMap.memSobolevproof · cited by 0