Abstract
We prove a generalization of the infinitesimal portion of the classical Schwarz lemma for functions from the polydisk to the disk. In particular, we describe the functions which play the role of automorphisms of the disk in this context–they turn out to be rational inner functions in the Schur-Agler class of the polydisk with an added symmetry constraint. In addition, some sufficient conditions are given for a function to be of this type.
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