Theorems · Theorem · complex analysis

AnalyticOnNhd.eval_linearMap

∀ {𝕜 : Type u_1} {E : Type u_2} {B : Type u_4} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedCommRing B] [inst_4 : NormedAlgebra 𝕜 B] {σ : Type u_5} [CompleteSpace 𝕜]
  [T2Space E] [FiniteDimensional 𝕜 E] (f : E →ₗ[𝕜] σ → B) (p : MvPolynomial σ B),
  AnalyticOnNhd 𝕜 (fun x => (MvPolynomial.eval (f x)) p) Set.univ

Defined in

Mathlib.Analysis.Analytic.Polynomial

Cited by

2 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedCommRingNormedAlgebraCompleteSpaceT2SpaceFiniteDimensional