Theorems · Theorem · real analysis

LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_right

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {s : Set E} (g : G ≃ₗᵢ[𝕜] E) (f : E → F),
  UniqueDiffOn 𝕜 s →
    ∀ {x : G},
      g x ∈ s → ∀ (i : ℕ), ‖iteratedFDerivWithin 𝕜 i (f ∘ ⇑g) (⇑g ⁻¹' s) x‖ = ‖iteratedFDerivWithin 𝕜 i f s (g x)‖

Composition with a linear isometry on the right preserves the norm of the iterated derivative within a set.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Basic

Cited by

3 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace