Extremal quasiconformality vs bounded rational approximation

• Published in: Український математичний вісник
• Date: 2019
• ISSN: 1810-3200
• Main Author: Krushkal, S.L.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/169439
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Extremal quasiconformality vs bounded rational approximation / S.L. Krushkal // Український математичний вісник. — 2019. — Т. 16, № 2. — С. 181-199. — Бібліогр.: 26 назв. — англ.

We show that, on most of the hyperbolic simply connected domains, the weighty bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorphic functions (in contrast to the integral approximation). The obstructions are caused by the features of extremal quas...