Theorems · Theorem · functional analysis
TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_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] {g₁ g₂ : E → ℂ},
Function.HasTemperateGrowth g₁ →
Function.HasTemperateGrowth g₂ →
∀ (f : TemperedDistribution E F),
(TemperedDistribution.fourierMultiplierCLM F g₂) ((TemperedDistribution.fourierMultiplierCLM F g₁) f) =
(TemperedDistribution.fourierMultiplierCLM F (g₁ * g₂)) f- Cited by
- 5 results in Mathlib
- Foundations
- Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommGroupproof · cited by 12,871
- NormedSpacestatement and proof · cited by 12,499
- Set.Elemstatement · cited by 7,166
- Set.ofPredstatement · cited by 6,101
Cited by5
Results whose statement or proof uses this declaration.
- TemperedDistribution.besselPotential_besselPotential_applyproof · cited by 3
- TemperedDistribution.besselPotential_neg_one_lineDerivOp_eqproof · cited by 1
- TemperedDistribution.besselPotential_neg_two_laplacian_eqproof · cited by 1
- TemperedDistribution.laplacian_eq_fourierMultiplierCLMproof · cited by 1
- TemperedDistribution.fourierMultiplierCLM_compL_fourierMultiplierCLMproof · cited by 0