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Bernstein- and Markov-type inequalities for rational functions

Sergei Kalmykov Shanghai Jiao Tong University Béla Nagy University of Szeged Vilmos Totik University of Szeged

Functional Analysis mathscidoc:1911.43014

Acta Mathematica, 219, (1), 21 – 63, 2017
Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on C2 smooth Jordan curves and arcs. The results are formulated in terms of the normal derivatives of certain Green’s functions with poles at the poles of the rational functions in question. As a special case (when all the poles are at infinity) the corresponding results for polynomials are recaptured.
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@inproceedings{sergei2017bernstein-,
  title={Bernstein- and Markov-type inequalities for rational functions},
  author={Sergei Kalmykov, Béla Nagy, and Vilmos Totik},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191126155947345903525},
  booktitle={Acta Mathematica},
  volume={219},
  number={1},
  pages={21 – 63},
  year={2017},
}
Sergei Kalmykov, Béla Nagy, and Vilmos Totik. Bernstein- and Markov-type inequalities for rational functions. 2017. Vol. 219. In Acta Mathematica. pp.21 – 63. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191126155947345903525.
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