Theorems · Theorem · harmonic analysis
Real.hasFDerivAt_fourierChar_neg_bilinear_right
∀ {V : Type u_1} {W : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [inst_2 : NormedAddCommGroup W]
[inst_3 : NormedSpace ℝ W] (L : V →L[ℝ] W →L[ℝ] ℝ) (v : V) (w : W),
HasFDerivAt (fun w => ↑(Real.fourierChar (-(L v) w)))
((-2 * ↑Real.pi * Complex.I * ↑(Real.fourierChar (-(L v) w))) • Complex.ofRealCLM ∘SL L v) w- Cited by
- 3 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommGroupproof · cited by 12,871
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldproof · cited by 8,742
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement and proof · cited by 5,352
- Submonoidstatement · cited by 3,086
Cited by3
Results whose statement or proof uses this declaration.
- Real.hasFDerivAt_fourierChar_neg_bilinear_leftproof · cited by 2
- Real.differentiable_fourierChar_neg_bilinear_rightproof · cited by 0
- Real.fderiv_fourierChar_neg_bilinear_right_applyproof · cited by 0