Branched circle packings and discrete Blaschke products

Author:
Tomasz Dubejko

Journal:
Trans. Amer. Math. Soc. **347** (1995), 4073-4103

MSC:
Primary 30D50; Secondary 30G25, 52C15

DOI:
https://doi.org/10.1090/S0002-9947-1995-1308008-1

MathSciNet review:
1308008

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we introduce the notion of discrete Blaschke products via circle packing. We first establish necessary and sufficient conditions for the existence of finite branched circle packings. Next, discrete Blaschke products are defined as circle packing maps from univalent circle packings that properly fill to the corresponding branched circle packings that properly cover . It is verified that such maps have all geometric properties of their classical counterparts. Finally, we show that any classical finite Blaschke product can be approximated uniformly on compacta of by discrete ones.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1308008-1

Keywords:
Circle packing,
Blaschke products,
discrete analytic functions

Article copyright:
© Copyright 1995
American Mathematical Society