Theorems · Theorem · potential theory

ContDiffAt.harmonicAt

∀ {F : Type u_1} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℂ F] {f : ℂ → F} {x : ℂ},
  ContDiffAt ℂ 2 f x → InnerProductSpace.HarmonicAt f x

Continuously complex-differentiable functions on ℂ are harmonic.

Defined in: Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions
Cited by: 1 results in Mathlib
Foundations: Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace

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AnalyticAt.harmonicAtproof · cited by 3