The higher order analogue of the classical Carathéodory-Julia theorem on boundary angular derivatives has been obtained in [7]. Here we study boundary interpolation problems for Schur class functions (analytic and bounded by one in the open unit disk) motivated by that result.1991 Mathematics Subject Classification. 47A57, 47A20, 47A48.In case n = 0, Theorem 1.1 reduces to the classical Carathéodory-Julia theorem [8,9]; this has been discussed in detail in [7]. The relationexpresses equality of the lower diagonal entries in (1.12); upon separating the term corresponding to i = n it can be written as(1.13) Theorem 1.

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A higher order analogue of the classical Carathéodory-Julia theorem on boundary derivatives is proved.

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