Theorems · Definition · potential theory
InnerProductSpace.HarmonicOnNhd
{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 → PropLet E be a real, finite-dimensional, inner product space and s be a subset of E. A function
f on E is harmonic in a neighborhood of s if it is harmonic at every point of s.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 244 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- InnerProductSpacestatement and proof · cited by 3,523
- FiniteDimensionalstatement and proof · cited by 1,854
- InnerProductSpace.HarmonicAtproof · cited by 23
Cited by26
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicContOnCl.harmonicOnNhdstatement · cited by 10
- InnerProductSpace.HarmonicOnNhd.circleAverage_eqstatement and proof · cited by 5
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqstatement and proof · cited by 4
- InnerProductSpace.HarmonicOnNhd.monostatement and proof · cited by 4
- InnerProductSpace.HarmonicOnNhd.circleAverage_re_herglotzRieszKernel_smulstatement and proof · cited by 2
- InnerProductSpace.HarmonicOnNhd.comp_CLMstatement and proof · cited by 2
- InnerProductSpace.HarmonicOnNhd.continuousOnstatement and proof · cited by 2
- InnerProductSpace.HarmonicOnNhd.addstatement and proof · cited by 1
- InnerProductSpace.HarmonicOnNhd.const_smulstatement and proof · cited by 1
- InnerProductSpace.HarmonicOnNhd.contDiffOnstatement and proof · cited by 1
- InnerProductSpace.harmonicOnNhd_conststatement · cited by 1
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_univ_re_eqstatement and proof · cited by 1