Theorems · Theorem · harmonic analysis
hasSum_fourier_series_of_summable
∀ {T : ℝ} [hT : Fact (0 < T)] {f : C(AddCircle T, ℂ)},
Summable (fourierCoeff ⇑f) → HasSum (fun i => fourierCoeff (⇑f) i • fourier i) fIf the sequence of Fourier coefficients of f is summable, then the Fourier series converges
uniformly to f.
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 273 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.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
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- Complexstatement and proof · cited by 5,565
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- Summablestatement and proof · cited by 778
- HasSumstatement and proof · cited by 518
- AddSubgroup.zmultiplesstatement · cited by 493
- MeasureTheory.AEEqFun.castproof · cited by 380
Cited by1
Results whose statement or proof uses this declaration.
- has_pointwise_sum_fourier_series_of_summableproof · cited by 2