Theorems · Theorem · harmonic analysis
MeasureTheory.Lp.inner_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 : ↥(MeasureTheory.Lp F 2 MeasureTheory.volume))
(g : ↥(MeasureTheory.Lp F 2 MeasureTheory.volume)),
inner ℂ (FourierTransform.fourier f) (FourierTransform.fourier g) = inner ℂ f g- Defined in
- Mathlib.Analysis.Fourier.LpSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 310 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- InnerProductSpacestatement and proof · cited by 3,523
- AddSubgroupstatement · cited by 3,232
- CompleteSpacestatement and proof · cited by 2,532
- FiniteDimensionalstatement and proof · cited by 1,854
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Inner.innerstatement · cited by 1,089
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