Theorems · Theorem · harmonic analysis
ZMod.dft_comp_unitMul
∀ {N : ℕ} [inst : NeZero N] {E : Type u_1} [inst_1 : AddCommGroup E] [inst_2 : Module ℂ E] (Φ : ZMod N → E)
(u : (ZMod N)ˣ) (k : ZMod N), ZMod.dft (fun j => Φ (↑u * j)) k = ZMod.dft Φ (↑u⁻¹ * k)- Defined in
- Mathlib.Analysis.Fourier.ZMod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZeroAddCommGroupModule
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- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Complexstatement and proof · cited by 5,565
- LinearEquivstatement · cited by 3,317
- Unitsstatement and proof · cited by 2,804
- mul_commproof · cited by 2,262
- Units.valstatement and proof · cited by 1,966
- ZModstatement and proof · cited by 1,024
- Fintype.sum_equivproof · cited by 35
- ZMod.dftstatement · cited by 25
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