Theorems · Theorem · functional analysis
TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq
∀ {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)The distributional inverse Fourier transform and the classical inverse Fourier transform
coincide on 𝓢(E, F).
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
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- ContinuousLinearMapstatement and proof · cited by 5,352
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- TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eqproof · cited by 0