Theorems · Theorem · harmonic analysis
fourierSubalgebra_closure_eq_top
∀ {T : ℝ} [hT : Fact (0 < T)], fourierSubalgebra.topologicalClosure = ⊤The subalgebra of C(AddCircle T, ℂ) generated by fourier n for n ∈ ℤ is dense.
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 207 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.
Cites12
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
- Top.topstatement · cited by 9,680
- Complexstatement · cited by 5,565
- Factstatement and proof · cited by 2,726
- ContinuousMapstatement · cited by 2,491
- AddSubgroup.zmultiplesstatement · cited by 493
- StarSubalgebrastatement · cited by 194
- AddCirclestatement · cited by 189
- StarSubalgebra.topologicalClosurestatement · cited by 22
- fourierSubalgebrastatement and proof · cited by 3
- fourierSubalgebra_separatesPointsproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- span_fourier_closure_eq_topproof · cited by 1