Best M\"obius approximations of convex and concave mappings

Martin Chuaqui; Brad Osgood

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arXiv · 2308.03911

Best M\"obius approximations of convex and concave mappings

Martin Chuaqui·Brad Osgood

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Abstract

We study the best M\"obius approximations (BMA) to convex and concave conformal mappings of the disk, including the special case of mappings onto convex polygons. The crucial factor is the location of the poles of the BMAs. Finer details are possible in the case of polygons through special properties of Blaschke products and the prevertices of the mapping function.

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Martin Chuaqui, Brad Osgood. 2023-08-07. Best M\"obius approximations of convex and concave mappings. https://arxiv.org/abs/2308.03911

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