Theorems · Theorem · functional analysis
SchwartzMap.smulLeftCLM_apply
∀ {𝕜 : Type u_2} {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
[inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : NontriviallyNormedField 𝕜]
[inst_5 : NormedAlgebra ℝ 𝕜] [inst_6 : NormedSpace 𝕜 F] {g : E → 𝕜},
Function.HasTemperateGrowth g → ∀ (f : SchwartzMap E F), ⇑((SchwartzMap.smulLeftCLM F g) f) = fun x => g x • f x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- NormedAlgebrastatement and proof · cited by 1,165
- SchwartzMapstatement and proof · cited by 251
- Function.HasTemperateGrowthstatement and proof · cited by 88
- SchwartzMap.smulLeftCLMstatement · cited by 41
Cited by3
Results whose statement or proof uses this declaration.
- SchwartzMap.smulLeftCLM_apply_applyproof · cited by 12
- Distribution.TemperedDistribution.IsVanishingOn.smulLeftCLMproof · cited by 2
- SchwartzMap.tsupport_smulLeftCLM_subsetproof · cited by 0