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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Bolotnikov, V., Kheifets, A. Carathéodory-Julia type theorems for operator valued Schur functions. J Anal Math 106, 237–270 (2008). https://doi.org/10.1007/s11854-008-0049-x
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DOI: https://doi.org/10.1007/s11854-008-0049-x