Theorems · Theorem · functional analysis
SchwartzMap.differentiableAt
∀ {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) {x : E}, DifferentiableAt ℝ (⇑f) xEvery Schwartz function is differentiable at any point.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 197 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.
- 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
- DifferentiableAtstatement · cited by 617
- SchwartzMapstatement and proof · cited by 251
- Differentiable.differentiableAtproof · cited by 32
- SchwartzMap.differentiableproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- SchwartzMap.hasDerivAtproof · cited by 1
- SchwartzMap.hasFDerivAtproof · cited by 1
- SchwartzMap.lineDerivOp_applyproof · cited by 0