Theorems · Theorem · real analysis
iteratedFDerivWithin_eq_equiv_comp
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {n : ℕ} {f : 𝕜 → F} {s : Set 𝕜},
iteratedFDerivWithin 𝕜 n f s = ⇑(ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F) ∘ iteratedDerivWithin n f sWrite the iterated Fréchet derivative as the composition of a continuous linear equiv and the iterated derivative.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Setstatement and proof · cited by 53,352
- 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
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- LinearIsometryEquivstatement · cited by 748
- LinearIsometryEquiv.symmproof · cited by 287
- iteratedFDerivWithinstatement and proof · cited by 147
- iteratedDerivWithinstatement · cited by 122
- Function.comp_assocproof · cited by 41
Cited by4
Results whose statement or proof uses this declaration.
- iteratedDerivWithin_succproof · cited by 11
- contDiffOn_of_differentiableOn_derivproof · cited by 1
- contDiffOn_iff_continuousOn_differentiableOn_derivproof · cited by 1
- contDiffOn_of_continuousOn_differentiableOn_derivproof · cited by 0