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Estimates for derivatives of rational functions and the fourth Zolotarev problem


Author: A. L. Lukashov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 19 (2007), nomer 2.
Journal: St. Petersburg Math. J. 19 (2008), 253-259
MSC (2000): Primary 53A04; Secondary 52A40, 52A10
DOI: https://doi.org/10.1090/S1061-0022-08-00997-7
Published electronically: February 7, 2008
MathSciNet review: 2333900
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Abstract | References | Similar Articles | Additional Information

Abstract: An estimate is obtained for the derivatives of real rational functions that map a compact set on the real line to another set of the same kind. Many well-known inequalities (due to Bernstein, Bernstein-Szegő, V. S. Videnskiĭ, V. N. Rusak, and M. Baran-V. Totik) are particular cases of this estimate. It is shown that the estimate is sharp. With the help of the solution of the fourth Zolotarev problem, a class of examples is constructed in which the estimates obtained turn into identities.


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Additional Information

A. L. Lukashov
Affiliation: N. G. Chernyshevskiĭ Saratov State University, Astrakhanskaya 83, 410012, Saratov, Russia
Address at time of publication: Department of Mathematics, Fatih University, 34900 Büyükçekmece, Istanbul, Turkey
Email: alexeylukashov@yahoo.de

DOI: https://doi.org/10.1090/S1061-0022-08-00997-7
Keywords: Estimates of derivatives, optimal filter, Zolotarev problems
Received by editor(s): October 11, 2006
Published electronically: February 7, 2008
Additional Notes: Supported by RFBR (grant no. 07-01-00167)
Article copyright: © Copyright 2008 American Mathematical Society

American Mathematical Society