Theorems · Theorem · harmonic analysis
span_fourier_closure_eq_top
∀ {T : ℝ} [hT : Fact (0 < T)], (Submodule.span ℂ (Set.range fourier)).topologicalClosure = ⊤The linear span of the monomials fourier n is dense in C(AddCircle T, ℂ).
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Complexstatement and proof · cited by 5,565
- Set.rangestatement · cited by 4,705
- Factstatement and proof · cited by 2,726
- ContinuousMapstatement and proof · cited by 2,491
- Submodule.spanstatement · cited by 1,504
- AddSubgroup.zmultiplesstatement · cited by 493
- StarSubalgebraproof · cited by 194
- AddCirclestatement and proof · cited by 189
Cited by1
Results whose statement or proof uses this declaration.
- span_fourierLp_closure_eq_topproof · cited by 0