Theorems · Theorem · real analysis
iteratedDerivWithin_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},
iteratedDerivWithin n f s = ⇑(ContinuousMultilinearMap.piFieldEquiv 𝕜 (Fin n) F).symm ∘ iteratedFDerivWithin 𝕜 n f sWrite the iterated derivative as the composition of a continuous linear equiv and the iterated Fréchet derivative
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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 · cited by 1,016
- LinearIsometryEquivstatement · cited by 748
- LinearIsometryEquiv.symmstatement · cited by 287
- iteratedFDerivWithinstatement · cited by 147
- iteratedDerivWithinstatement and proof · cited by 122
- ContinuousMultilinearMap.piFieldEquivstatement · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- iteratedFDerivWithin_eq_equiv_compproof · cited by 4
- ContDiffOn.continuousOn_iteratedDerivWithinproof · cited by 2
- norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithinproof · cited by 1
- ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithinproof · cited by 1