Theorems · Theorem · harmonic analysis
UnitAddTorus.span_mFourierLp_closure_eq_top
∀ {d : Type u_1} [inst : Fintype d] {p : ENNReal} [inst_1 : Fact (1 ≤ p)],
p ≠ ⊤ → (Submodule.span ℂ (Set.range (UnitAddTorus.mFourierLp p))).topologicalClosure = ⊤For each 1 ≤ p < ∞, the linear span of the monomials mFourier n is dense in the Lᵖ space
of functions on UnitAddTorus d.
- Defined in
- Mathlib.Analysis.Fourier.AddCircleMulti
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 237 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- Submodulestatement · cited by 7,192
- Complexstatement and proof · cited by 5,565
- Set.rangestatement and proof · cited by 4,705
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- ContinuousMapproof · cited by 2,491
- Submodule.spanstatement and proof · cited by 1,504
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
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