Theorems · Theorem · functional analysis
SchwartzMap.lineDeriv_eq_fourierMultiplierCLM
∀ {E : Type u_3} {F : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
[inst_2 : InnerProductSpace ℝ E] [inst_3 : NormedSpace ℂ F] [inst_4 : FiniteDimensional ℝ E]
[inst_5 : MeasurableSpace E] [inst_6 : BorelSpace E] [CompleteSpace F] (m : E) (f : SchwartzMap E F),
LineDeriv.lineDerivOp m f = (2 * ↑Real.pi * Complex.I) • (SchwartzMap.fourierMultiplierCLM F fun x => inner ℝ x m) f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 303 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- FiniteDimensionalstatement and proof · cited by 1,854
- Real.pistatement and proof · cited by 1,774
Cited by1
Results whose statement or proof uses this declaration.
- SchwartzMap.laplacian_eq_fourierMultiplierCLMproof · cited by 0