Geodesic
Covering theorems for polynomials with curved majorants on two segments
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 97-109 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, covering theorems for analytic functions related to polynomials that have curved majorants on two symmetric intervals are proved. These theorems contain and complement some new and classical results for polynomials with constraints on one and two intervals. Bibl. 15 titles. 
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S. I. Kalmykov. Covering theorems for polynomials with curved majorants on two segments. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 97-109. http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a6/

[1] M. A. Lachance, “Bernstein and Markov inequalities for constrained polynomials”, Lect. Notes Math., 1045, 1984, 125–135 | DOI | MR

[2] Q. I. Rahman, G. Schmeisser, “Markoff type inequalities for curved majorants”, Numerical methods of approx. theory, 8 (1987), 169–183 | MR | Zbl

[3] V. N. Dubinin, S. I. Kalmykov, “Printsip mazhoratsii dlya meromorfnykh funktsii”, Mat. sb., 198:12 (2007), 37–46 | DOI | MR | Zbl

[4] S. I. Kalmykov, “Printsipy mazhoratsii i nekotorye neravenstva dlya polinomov i ratsionalnykh funktsii s predpisannymi polyusami”, Zap. nauchn. semin. POMI, 357, 2008, 143–157 | Zbl

[5] S. I. Kalmykov, “O polinomakh, imeyuschikh krivolineinuyu mazhorantu na dvukh otrezkakh”, Izv. vuzov. Matematika, 2009, no. 10, 72–75 | MR | Zbl

[6] Ya. L. Geronimus, Teoriya ortogonalnykh mnogochlenov, M., 1950

[7] A. L. Levin, E. B. Saff, “Potential theoretic tools polynomial and rational approximation”, Harmonic Analysis and Rational Approximation, Lect. Notes in Control and Inf. Sci., 327, 2006, 71–94 | DOI | MR | Zbl

[8] Yu. V. Sidorov, M. V. Fedoryuk, M. I. Shabunin, Lektsii po teorii funktsii kompleksnogo peremennogo, M., 1989 | MR

[9] K. Dochev, “O nekotorykh ekstremalnykh svoistvakh mnogochlenov”, Dokl. AN SSSR, 153:3 (1963), 519–521 | Zbl

[10] P. Borwein, Polynomials and Polynomial Inequalities, Springer-Verlag, N.Y., 1995 | MR

[11] V. N. Dubinin, “Konformnye otobrazheniya i neravenstva dlya algebraicheskikh polinomov”, Algebra i analiz, 13:5 (2001), 16–43 | MR | Zbl

[12] S. Stoilov, Teoriya funktsii kompleksnogo peremennogo, v. 2, M., 1962

[13] G. Sege, Ortogonalnye mnogochleny, M., 1962

[14] I. P. Mityuk, Simmetrizatsionnye metody i ikh primenenie v geometricheskoi teorii funktsii. Vvedenie v simmetrizatsionnye metody, Izd. Kubanskogo gos. un-ta, Krasnodar, 1980

[15] N. I. Akhiezer, Elementy teorii ellipticheskikh funktsii, M., 1970 | Zbl