FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
On the distortion theorems for algebraic polynomials |
V. N. Dubinin |
2011, issue 1, P. 28–36 |
Abstract |
| The applications of a boundary Schwarz lemma and the properties of the condenser capacity to some inequalities for polynomials and their derivatives are considered. We prove a new Bernstein-type inequality for the polynomials on a circle, two-sided estimates for the polynomials with constraints on their critical values, and two-sided estimates of the average distortion computed at zeros of the polynomials. |
Keywords: polynomials, critical points, critical values, Chebyshev polynomial, Bernstein-type inequality, distortion theorem, condenser capacity |
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References |
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