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A Note on Rational \(L^p\) Approximation on Jordan Curves

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Abstract

The precise asymptotics for the error of best rational approximation of meromorphic functions in integral norm is shown to be a consequence of a result of Gonchar and Rakhmanov. This reproves and extends a recent result of Baratchart, Stahl and Yattselev.

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References

  1. Baratchart, L., Stahl, H., Yattselev, M.: Weighted extremal domains and best rational approximation. Adv. Math. 2012, 357–407 (2012)

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  2. Gonchar, A.A., Rakhmanov, E.A.: Equilibrium distributions and the degree of rational approximation of analytic functions. Mat. Sb. (Russ.) 134(176), 306–352 (1987); English Transl. in Math. USSR Sb. 62, 305–348 (1989)

  3. Pommerenke, Ch.: Boundary Behavior of Conformal Mappings, Grundlehren der mathematischen Wissenschaften, 299. Springer, Berlin (1992)

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Authors and Affiliations

  1. MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged, Aradi v. tere 1, Szeged, 6720, Hungary

    Vilmos Totik

  2. Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Ave, CMC 342, Tampa, FL, 33620-5700, USA

    Vilmos Totik

Authors
  1. Vilmos Totik
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Correspondence to Vilmos Totik.

Additional information

Communicated by Andrei Martinez Finkelshtein.

This research was supported by the European Research Council Advanced Grant No. 267055.

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Totik, V. A Note on Rational \(L^p\) Approximation on Jordan Curves. Comput. Methods Funct. Theory 13, 425–431 (2013). https://doi.org/10.1007/s40315-013-0028-9

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  • DOI: https://doi.org/10.1007/s40315-013-0028-9

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