On higher order boundary derivatives of an analytic self-map of the unit disk Original Research Article

Characterization of Schur-class functions (analytic and bounded by one in modulus on the open unit disk) in terms of their Taylor coefficients at the origin is due to I. Schur. We present a boundary analog of this result: necessary and sufficient conditions are given for the existence of a Schur-class function with the prescribed nontangential boundary expansi