InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_univ_re_eq

∀ {f : ℂ → ℝ}, InnerProductSpace.HarmonicOnNhd f Set.univ → ∃ F, AnalyticOnNhd ℂ F Set.univ ∧ (fun z => (F z).re) = f

If a function f : ℂ → ℝ is harmonic, then f is the real part of a holomorphic function.

Defined in: Mathlib.Analysis.Complex.Harmonic.Analytic
Cited by: 1 results in Mathlib
Foundations: Depth 291 from the axioms · uses propext, Classical.choice, Quot.sound

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