Theorems · Theorem · harmonic analysis
Real.fourierTransform_toLp
∀ {V : Type u_1} {E : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [inst_2 : NormedAddCommGroup V]
[inst_3 : InnerProductSpace ℝ V] [inst_4 : MeasurableSpace V] [inst_5 : BorelSpace V] [inst_6 : FiniteDimensional ℝ V]
{f : V → E} (hf : MeasureTheory.MemLp f 1 MeasureTheory.volume),
⇑(Real.Lp.fourierTransform (MeasureTheory.MemLp.toLp f hf)) = FourierTransform.fourier f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- Complexstatement and proof · cited by 5,565
- InnerProductSpacestatement and proof · cited by 3,523
- FiniteDimensionalstatement and proof · cited by 1,854
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- BoundedContinuousFunctionstatement · cited by 511
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