Abstract
We extend the Carathéodory-Julia theorem on angular derivatives as well as its higher order analogue established recently in [4] to the setting of contractive valued functions analytic on the unit disk. Carathéodory-Julia type conditions for an operator valued Schur-class function w are shown to be equivalent to the requirement that every function from the de Branges-Rovnyak space associated with w has certain directional boundary angular derivatives.
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