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Mat. Sb., 2000, Volume 191, Number 12, Pages 51–60 (Mi msb528)  

This article is cited in 11 scientific papers (total in 11 papers)

Distortion theorems for polynomials on a circle

V. N. Dubinin

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: Inequalities for the derivatives with respect to $\varphi=\arg z$ the functions $\operatorname{Re}P(z)$, $|P(z)|^2$ and $\arg P(z)$ are established for an algebraic polynomial $P(z)$ at points on the circle $|z|=1$. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial $P(z)$ and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli.

DOI: https://doi.org/10.4213/sm528

Full text: PDF file (246 kB)
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English version:
Sbornik: Mathematics, 2000, 191:12, 1797–1807

Bibliographic databases:

UDC: 517.54+512.62
MSC: Primary 30C10, 30A10; Secondary 30C85
Received: 14.12.1999 and 27.07.2000

Citation: V. N. Dubinin, “Distortion theorems for polynomials on a circle”, Mat. Sb., 191:12 (2000), 51–60; Sb. Math., 191:12 (2000), 1797–1807

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

    This publication is cited in the following articles:
    1. V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials. II”, J. Math. Sci. (N. Y.), 129:3 (2005), 3823–3834  mathnet  crossref  mathscinet  zmath
    2. A. V. Olesov, “Inequalities for majorizing analytical functions”, J. Math. Sci. (N. Y.), 133:6 (2006), 1693–1703  mathnet  crossref  mathscinet  zmath  elib
    3. A. V. Olesov, “Inequalities for entire functions of finite degree and polynomials”, J. Math. Sci. (N. Y.), 133:6 (2006), 1704–1717  mathnet  crossref  mathscinet  zmath  elib  elib
    4. A. V. Olesov, “Application of Conformal Mappings to Inequalities for Trigonometric Polynomials”, Math. Notes, 76:3 (2004), 368–378  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. N. Dubinin, “Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros”, J. Math. Sci. (N. Y.), 143:3 (2007), 3069–3076  mathnet  crossref  mathscinet  zmath  elib  elib
    6. Dubinin V.N., Karp D.B., “Generalized condensers and distortion theorems for conformal mappings of planar domains”, Interaction of Analysis and Geometry, Contemporary Mathematics Series, 424, 2007, 33–51  crossref  mathscinet  zmath  isi
    7. V. N. Dubinin, “K teoremam iskazheniya dlya algebraicheskikh polinomov”, Dalnevost. matem. zhurn., 11:1 (2011), 28–36  mathnet  elib
    8. V. N. Dubinin, “Lower Bound for the Discrete Norm of a Polynomial on the Circle”, Math. Notes, 90:2 (2011), 284–287  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. S. I. Kalmykov, “On polynomials and rational functions normalized on the circular arcs”, J. Math. Sci. (N. Y.), 200:5 (2014), 577–585  mathnet  crossref
    11. Wali S.L., Shah W.M., “Some applications of Dubinin's lemma to rational functions with prescribed poles”, J. Math. Anal. Appl., 450:1 (2017), 769–779  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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