St. Petersburg Mathematical Society

Estimates for derivatives of rational functions and the fourth Zolotarev problem

Author(s): 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
Posted: February 7, 2008
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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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Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 53A04, 52A40, 52A10

A. L. Lukashov
Affiliation: N. G. Chernyshevskii 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: 10.1090/S1061-0022-08-00997-7
PII: S 1061-0022(08)00997-7
Keywords: Estimates of derivatives, optimal filter, Zolotarev problems
Received by editor(s): 11/OCT/2006
Posted: February 7, 2008
Additional Notes: Supported by RFBR (grant no.~07-01-00167)
Copyright of article: Copyright 2008, American Mathematical Society

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ISSN: 1547-7371(e) ISSN: 1061-0022(p)

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