A. L. Lukashov, “Estimates for derivatives of rational functions and the fourth Zolotarev problem”, Algebra i Analiz, 19:2 (2007), 122–130; St. Petersburg Math. J., 19:2 (2008), 253

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Algebra i Analiz, 2007, Volume 19, Issue 2, Pages 122–130 (Mi aa116)

This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

Estimates for derivatives of rational functions and the fourth Zolotarev problem

A. L. Lukashov^ab

^a Saratov State University named after N. G. Chernyshevsky
^b Department of Mathematics, Fatih University, Istanbul, Turkey

Full-text PDF (141 kB) Citations (9)

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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—Szegö, V. S. Videnskii, 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.

Keywords: Estimates of derivatives, optimal filter, Zolotarev problems.

Received: 11.10.2006

English version:
St. Petersburg Mathematical Journal, 2008, Volume 19, Issue 2, Pages 253–259
DOI: https://doi.org/10.1090/S1061-0022-08-00997-7

Bibliographic databases:

Document Type: Article

MSC: Primary 53A04; Secondary 52A40, 52A10

Language: Russian

Citation: A. L. Lukashov, “Estimates for derivatives of rational functions and the fourth Zolotarev problem”, Algebra i Analiz, 19:2 (2007), 122–130; St. Petersburg Math. J., 19:2 (2008), 253–259

Citation in format AMSBIB

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\jour St. Petersburg Math. J.

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Linking options:

https://www.mathnet.ru/eng/aa116

https://www.mathnet.ru/eng/aa/v19/i2/p122

This publication is cited in the following 9 articles:

Lukashov A.L., Szabados J., “The order of Lebesgue constant of Lagrange interpolation on several intervals”, Period. Math. Hung., 72:2 (2016), 103–111
Totik V., “Bernstein- and Markov-Type Inequalities For Trigonometric Polynomials on General Sets”, Int. Math. Res. Notices, 2015, no. 11, 2986–3020
A. V. Olesov, “Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials”, Sb. Math., 205:10 (2014), 1413–1441
V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684
Totik V., “Bernstein-type inequalities”, J. Approx. Theory, 164:10 (2012), 1390–1401
S. I. Kalmykov, “Majoration principles and some inequalities for polynomials and rational functions with prescribed poles”, J. Math. Sci. (N. Y.), 157:4 (2009), 623–631
V. N. Dubinin, D. B. Karp, V. A. Shlyk, “Izbrannye zadachi geometricheskoi teorii funktsii i teorii potentsiala”, Dalnevost. matem. zhurn., 8:1 (2008), 46–95
V. N. Dubinin, “Emkosti kondensatorov i printsipy mazhoratsii v geometricheskoi teorii funktsii kompleksnogo peremennogo [Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke”]”, Sib. elektron. matem. izv., 5 (2008), 465–482
V. N. Dubinin, S. I. Kalmykov, “A majoration principle for meromorphic functions”, Sb. Math., 198:12 (2007), 1737–1745

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	70
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