Theorems · Theorem · functional analysis

ContinuousMultilinearMap.norm_iteratedFDerivComponent_le

∀ {𝕜 : Type u} {ι : Type v} {E₁ : ι → Type wE₁} {G : Type wG} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : (i : ι) → SeminormedAddCommGroup (E₁ i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E₁ i)]
  [inst_3 : SeminormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 G] [inst_5 : Fintype ι] {α : Type u_1}
  [inst_6 : Fintype α] (f : ContinuousMultilinearMap 𝕜 E₁ G) {s : Set ι} (e : α ≃ ↑s)
  [inst_7 : DecidablePred fun x => x ∈ s] (x : (i : ι) → E₁ i),
  ‖(f.iteratedFDerivComponent e) fun x_1 => x ↑x_1‖ ≤ ‖f‖ * ‖x‖ ^ (Fintype.card ι - Fintype.card α)

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Basic

Cited by

1 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceFintypeFintypeDecidablePred