Theorems · Theorem · harmonic analysis
fourierCoeff_toLp
∀ {T : ℝ} [hT : Fact (0 < T)] (f : C(AddCircle T, ℂ)) (n : ℤ),
fourierCoeff (↑↑((ContinuousMap.toLp 2 AddCircle.haarAddCircle ℂ) f)) n = fourierCoeff (⇑f) n- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 253 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.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
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- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- ContinuousMapstatement and proof · cited by 2,491
- MeasureTheory.AEEqFunstatement · cited by 856
- MeasureTheory.Lpstatement · cited by 715
- Filter.Eventually.of_forallproof · cited by 526
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.sum_sq_norm_coeff_eq_circleAverageproof · cited by 1
- hasSum_fourier_series_of_summableproof · cited by 1