Theorems · Theorem · complex analysis
FormalMultilinearSeries.ofScalars_norm_eq_mul
∀ {𝕜 : Type u_1} (E : Type u_2) [inst : NontriviallyNormedField 𝕜] [inst_1 : SeminormedRing E]
[inst_2 : NormedAlgebra 𝕜 E] (c : ℕ → 𝕜) (n : ℕ),
‖FormalMultilinearSeries.ofScalars E c n‖ = ‖c n‖ * ‖ContinuousMultilinearMap.mkPiAlgebraFin 𝕜 n E‖- Defined in
- Mathlib.Analysis.Analytic.OfScalars
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- NormedAlgebrastatement and proof · cited by 1,165
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- SeminormedRingstatement and proof · cited by 446
- norm_smulproof · cited by 242
- FormalMultilinearSeries.ofScalarsstatement · cited by 68
- ContinuousMultilinearMap.mkPiAlgebraFinstatement and proof · cited by 29
Cited by5
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendstoproof · cited by 3
- FormalMultilinearSeries.ofScalars_norm_leproof · cited by 2
- FormalMultilinearSeries.ofScalars_normproof · cited by 2
- alternatingGeometricSeries_apply_normproof · cited by 0
- alternatingGeometricSeries_apply_norm_leproof · cited by 0