Theorems · Inductive type · potential theory
InnerProductSpace.HarmonicContOnCl
{E : Type u_1} →
[inst : NormedAddCommGroup E] →
[inst_1 : InnerProductSpace ℝ E] →
[FiniteDimensional ℝ E] →
{F : Type u_2} → [inst : NormedAddCommGroup F] → [NormedSpace ℝ F] → (E → F) → Set E → PropA predicate saying that a function is harmonic on a set and is continuous on its closure. This is a common assumption in harmonic analysis.
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement · cited by 15,752
- NormedSpacestatement · cited by 12,499
- InnerProductSpacestatement · cited by 3,523
- FiniteDimensionalstatement · cited by 1,854
Cited by34
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicContOnCl.harmonicOnNhdstatement and proof · cited by 10
- InnerProductSpace.HarmonicContOnCl.continuousOnstatement and proof · cited by 9
- InnerProductSpace.harmonicContOnCl_conststatement · cited by 4
- InnerProductSpace.HarmonicContOnCl.substatement and proof · cited by 3
- InnerProductSpace.HarmonicContOnCl.addstatement and proof · cited by 3
- InnerProductSpace.HarmonicContOnCl.circleAverage_re_herglotzRieszKernel_smulstatement and proof · cited by 2
- InnerProductSpace.HarmonicContOnCl.negstatement and proof · cited by 1
- InnerProductSpace.HarmonicContOnCl.sub_conststatement and proof · cited by 1
- InnerProductSpace.HarmonicOnNhd.harmonicContOnClstatement · cited by 1
- InnerProductSpace.HarmonicContOnCl.add_conststatement and proof · cited by 1
- InnerProductSpace.HarmonicContOnCl.circleAverage_eqstatement and proof · cited by 1
- InnerProductSpace.HarmonicContOnCl.comp_CLMstatement and proof · cited by 1