Theorems · Theorem · functional analysis

TemperedDistribution.laplacian_apply_apply

∀ {E : Type u_3} {F : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E]
  [inst_2 : FiniteDimensional ℝ E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℂ F]
  (f : TemperedDistribution E F) (u : SchwartzMap E ℂ), (Laplacian.laplacian f) u = f (Laplacian.laplacian u)

Defined in: Mathlib.Analysis.Distribution.TemperedDistribution
Cited by: 1 results in Mathlib
Foundations: Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace FiniteDimensional NormedAddCommGroup NormedSpace

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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 · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
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
Finset.sumproof · cited by 5,195
InnerProductSpacestatement and proof · cited by 3,523
Finset.univproof · cited by 3,473

Cited by1

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TemperedDistribution.laplacian_toTemperedDistributionCLM_eqproof · cited by 0