By Jonathan E. Shapiro
This paper appears in the Journal of Operator Theory, 49 (2003), 85-97.
The notion of the angular derivative of a holomorphic self-map b
of the unit disk has been generalized to that of an angular derivative of
b relative to an inner function u. In this paper, we provide
three more conditions equivalent to the existence of an angular derivative
of b relative to u, and use these notions to provide a generalization
of Julia's lemma.
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