In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes as values strict contractions.
@article{bwmeta1.element.bwnjournal-article-apmv66z1p239bwm,
author = {Ion Suciu},
title = {Analytic formulas for the hyperbolic distance between two contractions},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {239-252},
zbl = {0873.47006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p239bwm}
}
Ion Suciu. Analytic formulas for the hyperbolic distance between two contractions. Annales Polonici Mathematici, Tome 66 (1997) pp. 239-252. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p239bwm/
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