Theorems · Theorem · complex analysis

MeromorphicOn.divisor_closedBall_comp_sub_const_eq_divisor_closedBall

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {z : 𝕜} {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {c : 𝕜} {R : ℝ} {f : 𝕜 → E},
  (MeromorphicOn.divisor (f ∘ fun x => x - c) (Metric.closedBall c R)) (z + c) =
    (MeromorphicOn.divisor f (Metric.closedBall 0 R)) z

Divisors are invariant under translation, special case where the set is a closed ball.

Defined in

Mathlib.Analysis.Meromorphic.Divisor

Cited by

1 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace