Theorems · Theorem · functional analysis
SchwartzMap.smooth
∀ {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] (f : SchwartzMap E F) (n : ℕ∞), ContDiff ℝ ↑n ⇑fEvery Schwartz function is smooth.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 195 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 · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENatstatement and proof · cited by 4,985
- WithTop.somestatement · cited by 1,128
- le_topproof · cited by 411
- ContDiffstatement · cited by 352
- SchwartzMapstatement and proof · cited by 251
- ContDiff.of_leproof · cited by 18
- SchwartzMap.smooth'proof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- SchwartzMap.continuousproof · cited by 7
- SchwartzMap.differentiableproof · cited by 2
- SchwartzMap.integrable_pow_mul_iteratedFDerivproof · cited by 1
- SchwartzMap.hasTemperateGrowthproof · cited by 1
- SchwartzMap.iteratedLineDerivOp_eq_iteratedFDerivproof · cited by 0
- SchwartzMap.contDiffAtproof · cited by 0