norm_fderivWithin_iteratedFDerivWithin

English

The operator norm of fderivWithin equals the norm of the (n+1)-th iterated derivative.

Русский

Ободу нормa fderivWithin равна норме (n+1)-й итеративной производной.

LaTeX

$$$$\|fderivWithin\(\mathbb{k}, (\text{iteratedFDerivWithin}(\mathbb{k},n,f,s)\,s)\,(x)\| = \| iteratedFDerivWithin(\mathbb{k},n+1,f,s)(x)\|.$$$$

Lean4

theorem norm_fderivWithin_iteratedFDerivWithin {n : ℕ} :
    ‖fderivWithin 𝕜 (iteratedFDerivWithin 𝕜 n f s) s x‖ = ‖iteratedFDerivWithin 𝕜 (n + 1) f s x‖ := by
  rw [iteratedFDerivWithin_succ_eq_comp_left, comp_apply, LinearIsometryEquiv.norm_map]

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