Theorems · Theorem · functional analysis

TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq

Deprecated since 2026-01-14Use TemperedDistribution.fourier_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),
  FourierTransform.fourier ((SchwartzMap.toTemperedDistributionCLM E F MeasureTheory.volume) f) =
    (SchwartzMap.toTemperedDistributionCLM E F MeasureTheory.volume) (FourierTransform.fourier f)

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

Defined in: Mathlib.Analysis.Distribution.TemperedDistribution
Cited by: 0 results in Mathlib
Foundations: Depth 302 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
Realstatement · cited by 25,697
RingHom.idstatement · cited by 18,349
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ContinuousLinearMapstatement · cited by 5,352
InnerProductSpacestatement · cited by 3,523

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