Theorems · Theorem · several complex variables

HasFPowerSeriesWithinOnBall.compContinuousLinearMap

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} {F : Type u_4} {G : Type u_5}
  [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] {u : E →L[𝕜] F} {f : F → G}
  {pf : FormalMultilinearSeries 𝕜 F G} {s : Set F} {x : E} {r : ENNReal},
  HasFPowerSeriesWithinOnBall f pf s (u x) r →
    HasFPowerSeriesWithinOnBall (f ∘ ⇑u) (pf.compContinuousLinearMap u) (⇑u ⁻¹' s) x (r / ‖u‖ₑ)

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace