Theorems · Theorem · functional analysis
TemperedDistribution.fourierMultiplierCLM_apply_apply
∀ {E : Type u_3} {F : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
[inst_2 : InnerProductSpace ℝ E] [inst_3 : NormedSpace ℂ F] [inst_4 : FiniteDimensional ℝ E]
[inst_5 : MeasurableSpace E] [inst_6 : BorelSpace E] (g : E → ℂ) (f : TemperedDistribution E F) (u : SchwartzMap E ℂ),
((TemperedDistribution.fourierMultiplierCLM F g) f) u =
f (FourierTransform.fourier ((SchwartzMap.smulLeftCLM ℂ g) (FourierTransformInv.fourierInv u)))- Cited by
- 3 results in Mathlib
- Foundations
- Depth 304 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- Set.Elemstatement · cited by 7,166
- Set.ofPredstatement · cited by 6,101
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
Cited by3
Results whose statement or proof uses this declaration.
- TemperedDistribution.fourierMultiplierCLM_constproof · cited by 1
- TemperedDistribution.fourierMultiplierCLM_sumproof · cited by 1
- TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eqproof · cited by 1