Theorems · Theorem · harmonic analysis
fourierSubalgebra_coe
∀ {T : ℝ}, Subalgebra.toSubmodule fourierSubalgebra.toSubalgebra = Submodule.span ℂ (Set.range fourier)The star subalgebra of C(AddCircle T, ℂ) generated by fourier n for n ∈ ℤ is in fact the
linear span of these functions.
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- SetLike.coeproof · cited by 8,199
- Submodulestatement · cited by 7,192
- Complexstatement and proof · cited by 5,565
- Set.rangestatement and proof · cited by 4,705
- ContinuousMapstatement and proof · cited by 2,491
- Submodule.spanstatement · cited by 1,504
- Subalgebrastatement · cited by 1,353
- OrderEmbeddingstatement · cited by 619
- AddSubgroup.zmultiplesstatement · cited by 493
- Submodule.subset_spanproof · cited by 234
Cited by1
Results whose statement or proof uses this declaration.
- span_fourier_closure_eq_topproof · cited by 1