Theorems · Theorem · functional analysis
SchwartzMap.smulLeftCLM_smul
∀ {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 → ∀ (c : 𝕜), SchwartzMap.smulLeftCLM F (c • g) = c • SchwartzMap.smulLeftCLM F g- Cited by
- 3 results in Mathlib
- Foundations
- Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- RingHom.idstatement and proof · 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 and proof · cited by 5,352
- NormedAlgebrastatement and proof · cited by 1,165
- ContinuousLinearMap.compproof · cited by 709
- SchwartzMapstatement and proof · cited by 251
- ContinuousLinearMap.idproof · cited by 233
- Function.HasTemperateGrowthstatement and proof · cited by 88
- ContinuousLinearMap.comp.congr_simpproof · cited by 77
Cited by3
Results whose statement or proof uses this declaration.
- TemperedDistribution.smulLeftCLM_smulproof · cited by 1
- SchwartzMap.fourierMultiplierCLM_smulproof · cited by 0
- SchwartzMap.smulLeftCLM_real_smulproof · cited by 0