Theorems · Theorem · several complex variables
ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall
∀ {𝕜 : Type u_1} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {ι : Type u_5} {Em : ι → Type u_6} [inst_3 : (i : ι) → NormedAddCommGroup (Em i)]
[inst_4 : (i : ι) → NormedSpace 𝕜 (Em i)] [inst_5 : Fintype ι] (f : ContinuousMultilinearMap 𝕜 Em F),
HasFiniteFPowerSeriesOnBall (⇑f) f.toFormalMultilinearSeries 0 (Fintype.card ι + 1) ⊤- Defined in
- Mathlib.Analysis.Analytic.CPolynomial
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Fintypestatement and proof · cited by 7,736
- zero_addproof · cited by 2,366
- Fintype.cardstatement and proof · cited by 1,386
- Finset.rangeproof · cited by 1,341
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- LT.lt.neproof · cited by 872
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.hasStrictFDerivAtproof · cited by 4
- ContinuousMultilinearMap.cpolynomialAtproof · cited by 3