Theorems · Theorem · harmonic analysis

SchwartzMap.toLp_fourier_eq

∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : MeasurableSpace E] [inst_2 : BorelSpace E]
  [inst_3 : NormedAddCommGroup F] [inst_4 : InnerProductSpace ℂ F] [inst_5 : CompleteSpace F]
  [inst_6 : InnerProductSpace ℝ E] [inst_7 : FiniteDimensional ℝ E] (f : SchwartzMap E F),
  FourierTransform.fourier (f.toLp 2 MeasureTheory.volume) = (FourierTransform.fourier f).toLp 2 MeasureTheory.volume

Defined in: Mathlib.Analysis.Fourier.LpSpace
Cited by: 1 results in Mathlib
Foundations: Depth 310 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup MeasurableSpace BorelSpace NormedAddCommGroup InnerProductSpace CompleteSpace InnerProductSpace FiniteDimensional

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Cites29

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
ENNRealstatement · cited by 9,879
Complexstatement and proof · cited by 5,565
Norm.normproof · cited by 5,413
InnerProductSpacestatement and proof · cited by 3,523
AddSubgroupstatement · cited by 3,232
one_mulproof · cited by 2,841
CompleteSpacestatement and proof · cited by 2,532
FiniteDimensionalstatement and proof · cited by 1,854

Cited by1

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MeasureTheory.Lp.fourier_toTemperedDistribution_eqproof · cited by 2