Theorems · Theorem · functional analysis
Function.HasTemperateGrowth.mul
∀ {R : Type u_3} {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedRing R]
[inst_3 : NormedAlgebra ℝ R] {f g : E → R},
Function.HasTemperateGrowth f → Function.HasTemperateGrowth g → Function.HasTemperateGrowth (f * g)The product of two functions of temperate growth is again of temperate growth.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NormedSpacestatement and proof · cited by 12,499
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- Function.HasTemperateGrowthstatement and proof · cited by 88
- ContinuousLinearMap.mulproof · cited by 63
- ContinuousLinearMap.bilinear_hasTemperateGrowthproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- SchwartzMap.smulLeftCLM_smulLeftCLM_applyproof · cited by 3
- Function.HasTemperateGrowth.fun_mulproof · cited by 2
- Function.HasTemperateGrowth.powproof · cited by 1