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• W2008821659 abstract "Let f be holomorphically continuable over the complex plane except for finitely many poles and branch points contained in the unit disk. We prove that best rational approximants to f of degree n, in the L2-sense on the unit circle, have poles that asymptotically distribute according to the equilibrium measure on the compact set outside of which f is single-valued and which has minimal Green capacity in the disk among all such sets. This provides us with n-th root asymptotics of the approximation error. By conformal mapping, we deduce further estimates in approximation by rational or meromorphic functions to f in the L2-sense on more general Jordan curves encompassing the poles and branch points. The key to these approximation-theoretic results is a characterization of extremal domains of holomorphy for f in the sense of a weighted logarithmic potential, which is the technical core of the paper." @default.
• W2008821659 created "2016-06-24" @default.
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• W2008821659 date "2012-01-01" @default.
• W2008821659 modified "2023-10-16" @default.
• W2008821659 title "Weighted extremal domains and best rational approximation" @default.
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• W2008821659 doi "https://doi.org/10.1016/j.aim.2011.09.005" @default.
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