A Schwarz lemma on the polydisk

Details A Schwarz lemma on the polydisk A Schwarz lemma on the polydisk

2005-12-19

arxiv.org/abs/math/0512452v1

Mathematics

Complex Variables

12 pages. See also http://www.math.wustl.edu/~geknese

Scientific paper

There is a known generalization of the classical Schwarz lemma to holomorphic functions from the polydisk to the disk. In this paper, we characterize those functions which satisfy equality everywhere in this generalized inequality: they are the transfer function of an n+1 by n+1 symmetric unitary, and in particular, are rational, inner, and belong to the Schur-Agler class of the polydisk. We also present some sufficient conditions for a function to be of this type.

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