Theorems · Theorem · functional analysis
TemperedDistribution.laplacian_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] (f : TemperedDistribution E F),
Laplacian.laplacian f = -(2 * Real.pi) ^ 2 • (TemperedDistribution.fourierMultiplierCLM F fun x => ↑(‖x‖ ^ 2)) f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Finsetproof · cited by 13,712
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- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- Complexstatement and proof · cited by 5,565
Cited by1
Results whose statement or proof uses this declaration.
- TemperedDistribution.besselPotential_neg_two_laplacian_eqproof · cited by 1