Bernstein- and Markov-type Inequalities for Rational Functions

Authors

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

Document Type

Article

Publication Date

2017

Digital Object Identifier (DOI)

https://doi.org/10.4310/ACTA.2017.v219.n1.a3

Abstract

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.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Acta Mathematica, v. 219, issue 1, p. 21-63

Scholar Commons Citation

Kalmykov, Sergei; Nagy, Béla; and Totik, Vilmos, "Bernstein- and Markov-type Inequalities for Rational Functions" (2017). Mathematics and Statistics Faculty Publications. 64.
https://digitalcommons.usf.edu/mth_facpub/64