Radial and circular slit maps of unbounded multiply connected circle domains

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Authors
DeLillo, Thomas K.
Driscoll, T. A.
Elcrat, Alan R.
Pfaltzgraff, J. A.
Issue Date
2008-07-08
Type
Article
Language
en_US
Keywords
Conformal maps , Multiply connected domains , Canonical domains
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Abstract

Infinite product formulae for conformally mapping an unbounded multiply connected circle domain to an unbounded canonical radial or circular slit domain, or to domains with both radial and circular slit boundary components are derived and implemented numerically and graphically. The formulae are generated by analytic continuation with the reflection principle. Convergence of the infinite products is proved for domains with sufficiently well-separated boundary components. Some recent progress in the numerical implementation of infinite product mapping formulae is presented.

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Citation
DeLillo, T. K., T. A. Driscoll, et al. (2008). "Radial and circular slit maps of unbounded multiply connected circle domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 464(2095): 1719-1737.
Publisher
The Royal Society
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DOI
ISSN
1364-5021
1471-2946
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