Theorems · Theorem · functional analysis
TemperedDistribution.besselPotential_neg_one_lineDerivOp_eq
∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
[inst_2 : InnerProductSpace ℝ E] [inst_3 : FiniteDimensional ℝ E] [inst_4 : MeasurableSpace E] [inst_5 : BorelSpace E]
[inst_6 : NormedSpace ℂ F] {m : E} (f : TemperedDistribution E F),
(TemperedDistribution.besselPotential E F (-1)) (LineDeriv.lineDerivOp m f) =
(2 * ↑Real.pi * Complex.I) •
(TemperedDistribution.fourierMultiplierCLM F fun x => ↑(inner ℝ x m * (1 + ‖x‖ ^ 2) ^ (-1 / 2))) f- Defined in
- Mathlib.Analysis.Distribution.Sobolev
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · 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
- Set.Elemstatement · cited by 7,166
- Set.ofPredstatement · cited by 6,101
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement and proof · cited by 5,352
Cited by1
Results whose statement or proof uses this declaration.
- TemperedDistribution.MemSobolev.lineDerivOpproof · cited by 0