Theorems · Theorem · functional analysis
TemperedDistribution.laplacian_toTemperedDistributionCLM_eq
∀ {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]
[inst_5 : MeasurableSpace E] [inst_6 : BorelSpace E] (f : SchwartzMap E F),
Laplacian.laplacian ((SchwartzMap.toTemperedDistributionCLM E F MeasureTheory.volume) f) =
(SchwartzMap.toTemperedDistributionCLM E F MeasureTheory.volume) (Laplacian.laplacian f)The distributional Laplacian and the classical Laplacian coincide on 𝓢(E, F).
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- Foundations
- Depth 289 from the axioms · uses propext, Classical.choice, Quot.sound
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