# the “three-point” characterization of holomorphy

I want to know the source of the following "folkloric" fact about holomorphic functions. It seems well described by the phrase: The three-point characterization of holomorphy. If F is a self-map of the open unit disk D and for every three points in D there exists a holomorphic self-map f of D which agrees with F at each of these three points,then F is holomorphic in D. There is an "easy",but clever proof using only Schwarz' Lemma and Montel's compactness Theorem.

-