Theorems · Theorem · functional analysis

TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq

Deprecated since 2026-01-14Use TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq instead.

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

Alias of TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq. The distributional inverse Fourier transform and the classical inverse Fourier transform coincide on 𝓢(E, F).

Defined in: Mathlib.Analysis.Distribution.TemperedDistribution
Cited by: 0 results in Mathlib
Foundations: Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace FiniteDimensional MeasurableSpace BorelSpace NormedAddCommGroup NormedSpace CompleteSpace

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DFunLike.coestatement · cited by 62,936
Setstatement · cited by 53,352
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RingHom.idstatement · cited by 18,349
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InnerProductSpacestatement · cited by 3,523

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