On a multi-point Schwarz-Pick lemma
Kyung Hyun Cho, Seong-A Kim, Toshiyuki Sugawa
TL;DR
This paper explores the multi-point Schwarz-Pick lemma, analyzing its properties and connections to continued fractions and inequalities for bounded analytic functions in the unit disk.
Contribution
It provides a comprehensive summary of associate functions related to the multi-point Schwarz-Pick lemma and reveals their applications to classical algorithms and inequalities.
Findings
Associate functions exhibit key properties of the multi-point Schwarz-Pick lemma.
Special cases recover Schur's continued fraction algorithm.
Derives inequalities for bounded analytic functions on the unit disk.
Abstract
We consider the multi-point Schwarz-Pick lemma and its associate functions due to Beardon-Minda and Baribeau-Rivard-Wegert. Basic properties of the associate functions are summarized. Then we observe that special cases of the multi-point Schwarz-Pick lemma give Schur's continued fraction algorithm and several inequalities for bounded analytic functions on the unit disk.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Mathematical functions and polynomials