On a multi-point Schwarz-Pick Lemma

Hyun Kyung Cho; Seong A. Kim; Toshiyuki Sugawa

doi:10.1007/BF03321839

On a multi-point Schwarz-Pick Lemma

Hyun Kyung Cho, Seong A. Kim, Toshiyuki Sugawa

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 the Schur's continued fraction algorithm and several inequalities for bounded analytic functions on the unit disk.

Original language	English
Pages (from-to)	483-499
Number of pages	17
Journal	Computational Methods and Function Theory
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/BF03321839
Publication status	Published - 2012

Keywords

Dieudonńe's Lemma
Nevanlinna-Pick interpolation
Peschl's invariant derivative
Schur algorithm
Schwarz-Pick Lemma

ASJC Scopus subject areas

Analysis
Computational Theory and Mathematics
Applied Mathematics

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title = "On a multi-point Schwarz-Pick Lemma",

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 the Schur's continued fraction algorithm and several inequalities for bounded analytic functions on the unit disk.",

keywords = "Dieudon{\'n}e's Lemma, Nevanlinna-Pick interpolation, Peschl's invariant derivative, Schur algorithm, Schwarz-Pick Lemma",

author = "Cho, {Hyun Kyung} and Kim, {Seong A.} and Toshiyuki Sugawa",

note = "Funding Information: Received June 21, 2011, in revised forms January 14, 2012, and February 13, 2012. Published online August 21, 2012. The third author was supported in part by JSPS Grant-in-Aid for Scientific Research (B), 17340039 and for Exploratory Research, 19654027.",

year = "2012",

doi = "10.1007/BF03321839",

language = "English",

volume = "12",

pages = "483--499",

journal = "Computational Methods and Function Theory",

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TY - JOUR

T1 - On a multi-point Schwarz-Pick Lemma

AU - Cho, Hyun Kyung

AU - Kim, Seong A.

AU - Sugawa, Toshiyuki

N1 - Funding Information: Received June 21, 2011, in revised forms January 14, 2012, and February 13, 2012. Published online August 21, 2012. The third author was supported in part by JSPS Grant-in-Aid for Scientific Research (B), 17340039 and for Exploratory Research, 19654027.

PY - 2012

Y1 - 2012

N2 - 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 the Schur's continued fraction algorithm and several inequalities for bounded analytic functions on the unit disk.

AB - 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 the Schur's continued fraction algorithm and several inequalities for bounded analytic functions on the unit disk.

KW - Dieudonńe's Lemma

KW - Nevanlinna-Pick interpolation

KW - Peschl's invariant derivative

KW - Schur algorithm

KW - Schwarz-Pick Lemma

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U2 - 10.1007/BF03321839

DO - 10.1007/BF03321839

M3 - Article

AN - SCOPUS:84878624314

VL - 12

SP - 483

EP - 499

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

SN - 1617-9447

IS - 2

ER -

On a multi-point Schwarz-Pick Lemma

Abstract

Keywords

ASJC Scopus subject areas

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