Bell representations of finitely connected planar domains

Jeong, Moonja; Taniguchi, Masahiko

doi:10.1090/S0002-9939-02-06823-5

Bell representations of finitely connected planar domains
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by Moonja Jeong and Masahiko Taniguchi

Proc. Amer. Math. Soc. 131 (2003), 2325-2328

DOI: https://doi.org/10.1090/S0002-9939-02-06823-5

Published electronically: November 14, 2002

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Abstract:

In this paper, we solve a conjecture of S. Bell (1992) affirmatively. Actually, we prove that every non-degenerate $n$-connected planar domain $\Omega$, where $n>1$ is representable as $\Omega = \{|f|<1\}$ with a suitable rational function $f$ of degree $n$. This result is considered as a natural generalization of the classical Riemann mapping theorem for simply connected planar domains.

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