English

Bernstein- and Markov-type inequalities for rational functions

Complex Variables 2016-10-24 v1

Abstract

Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on C2C^2 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.

Keywords

Cite

@article{arxiv.1610.06706,
  title  = {Bernstein- and Markov-type inequalities for rational functions},
  author = {Sergei Kalmykov and Béla Nagy and Vilmos Totik},
  journal= {arXiv preprint arXiv:1610.06706},
  year   = {2016}
}

Comments

42 pages, 2 figures

R2 v1 2026-06-22T16:27:31.845Z