A Schwarz lemma on the polydisk
复变函数
2013-02-06 v1
摘要
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.
引用
@article{arxiv.math/0512452,
title = {A Schwarz lemma on the polydisk},
author = {Greg E. Knese},
journal= {arXiv preprint arXiv:math/0512452},
year = {2013}
}
备注
12 pages. See also http://www.math.wustl.edu/~geknese