Theorems · Theorem · functional analysis
SchwartzMap.laplacian_apply
∀ {E : Type u_5} {F : Type u_8} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace ℝ F]
[inst_3 : InnerProductSpace ℝ E] [inst_4 : FiniteDimensional ℝ E] (f : SchwartzMap E F) (x : E),
(Laplacian.laplacian f) x = Laplacian.laplacian (⇑f) x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Finset.sumproof · cited by 5,195
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankproof · cited by 1,770
- Matrix.vecEmptyproof · cited by 832
- SchwartzMapstatement and proof · cited by 251
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