Carathéodory–Julia type theorems for operator valued Schur functions
نویسنده
چکیده
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.
منابع مشابه
Carathéodory-Julia type conditions and sym- metries of boundary asymptotics for analytic functions on the unit disk
It is shown that the following conditions are equivalent for the generalized Schur class functions w at a boundary point t0 ∈ T: Carathéodory– Julia type condition of order n ([2], [3]); agreeing of asymptotics from inside and outside of the disk D up to order 2n+1 ([11]); t0-isometry of the coefficients of the boundary asymptotics; a certain structured matrix P constructed from these coefficie...
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تاریخ انتشار 2007