Geodesic
A Generalization of Jentzsch's Theorem
Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 753-758.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the asymptotic behavior of the roots of polynomials given by a linear summation method for partial sums of the Fourier series.
Keywords: Jentzsch's theorem, Fourier series, Bernstein polynomial, Cauchy bound, Vitali's theorem, Hurwitz theorem.
Mots-clés : polynomial, Laurent series 
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E. A. Lebedeva. A Generalization of Jentzsch's Theorem. Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 753-758. http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a9/

[1] R. Jentzsch, Untersuchungen zur Theorie der Folgen analytischer Funktionen, Inaugural-Dissertation, Berlin, 1914

[2] D. V. Khristoforov, “Ob asimptoticheskikh svoistvakh interpolyatsionnykh mnogochlenov”, Matem. zametki, 83:1 (2008), 129–138 | MR | Zbl

[3] I. Ya. Novikov, “Asimptotika kornei polinomov Bernshteina, ispolzuemykh v postroenii modifitsirovannykh vspleskov Dobeshi”, Matem. zametki, 71:2 (2002), 239–253 | MR | Zbl

[4] G. M. Fikhtengolts, Kurs integralnogo i differentsialnogo ischisleniya: v 3 t., v. 3, Fizmatlit, M., 1960 | Zbl

[5] H. K. Bari, Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[6] Q. I. Rahman, G. Schmeisser, Analytic Theory of Polynomials, London Math. Soc. Monogr. (N.S.), 26, Claredron Press, Oxford, 2002 | MR | Zbl

[7] V. V. Prasolov, Mnogochleny, MTsNMO, M., 2003