Theorems · Theorem · potential theory
AnalyticAt.harmonicAt_conj
∀ {x : ℂ} {f : ℂ → ℂ}, AnalyticAt ℂ f x → InnerProductSpace.HarmonicAt ((starRingEnd (ℂ → ℂ)) f) xIf f : ℂ → ℂ is complex-analytic, then its complex conjugate is harmonic.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- RingHomstatement · cited by 10,189
- Complexstatement and proof · cited by 5,565
- starRingEndstatement · cited by 671
- AnalyticAtstatement and proof · cited by 321
- InnerProductSpace.HarmonicAtstatement · cited by 23
- Complex.conjCLEproof · cited by 15
- AnalyticAt.harmonicAtproof · cited by 3
- InnerProductSpace.harmonicAt_comp_CLE_iffproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.