New extremal properties for constructing conformal mappings |
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Authors: | Gerhard Opfer |
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Institution: | (1) Institut für Angewandte Mathematik, Universität Hamburg, Bundesstr. 55, D-2000 Hamburg 13, Germany (Fed. Rep.) |
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Abstract: | Summary It is well known that for a given simply connected regionR containing zero the uniform norm
attains its minimum in the class of all holomorphic functions normalized byf(0)=0 andf(0)=1 only for the conformal mappingfRD(r)={z|z|}. It is shown that this theorem is still valid if one replaces the ordinary modulus | | on by any other norm on . For instance it is possible to obtain direct mappings ofR onto parallelograms, rectangles and ellipses. For the special norms |1 and | this leads to a simple and fast computational technique involving linear programming methods. Several numerical examples are given. |
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Keywords: | AMS(MOS) 30A28 30A38 |
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