Theorems · Theorem · functional analysis
TemperedDistribution.besselPotential_neg_two_laplacian_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] (f : TemperedDistribution E F),
(TemperedDistribution.besselPotential E F (-2)) (Laplacian.laplacian f) =
-(2 * Real.pi) ^ 2 • (TemperedDistribution.fourierMultiplierCLM F fun x => ↑(‖x‖ ^ 2 * (1 + ‖x‖ ^ 2) ^ (-1))) f- Defined in
- Mathlib.Analysis.Distribution.Sobolev
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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
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- NormedSpacestatement and proof · cited by 12,499
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- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement and proof · cited by 5,352
Cited by1
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- TemperedDistribution.MemSobolev.laplacianproof · cited by 0