Theorems · Theorem
FourierTransform.fourier_sum
∀ {ι : Type u_1} {E : Type u_3} {F : Type u_4} [inst : AddCommGroup E] [inst_1 : AddCommGroup F]
[inst_2 : FourierTransform E F] [FourierAdd E F] (f : ι → E) (s : Finset ι),
FourierTransform.fourier (∑ i ∈ s, f i) = ∑ i ∈ s, FourierTransform.fourier (f i)- Defined in
- Mathlib.Analysis.Fourier.Notation
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Finset.sumstatement · cited by 5,195
- map_sumproof · cited by 455
- FourierTransform.fourierstatement and proof · cited by 130
- AddMonoidHom.mk'proof · cited by 25
- FourierTransformstatement and proof · cited by 23
- FourierAddstatement and proof · cited by 14
- FourierAdd.fourier_addproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- TemperedDistribution.fourierMultiplierCLM_sumproof · cited by 1