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Mat. Zametki, 2004, Volume 76, Issue 3, Pages 396–408 (Mi mz116)  

This article is cited in 8 scientific papers (total in 8 papers)

Application of Conformal Mappings to Inequalities for Trigonometric Polynomials

A. V. Olesov

Maritime State University named after G. I. Nevelskoi

Abstract: In this paper, we obtain inequalities for trigonometric and algebraic polynomials supplementing and strengthening the classical results going back to papers of S. N. Bernstein and I. I. Privalov. The method of proof is based on the construction of the conformal and univalent mapping from a given trigonometric polynomial and on the application of results of the geometric theory of functions of a complex variable to this mapping.

DOI: https://doi.org/10.4213/mzm116

Full text: PDF file (214 kB)
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English version:
Mathematical Notes, 2004, 76:3, 368–378

Bibliographic databases:

UDC: 512.62+517.54
Received: 21.07.2003

Citation: A. V. Olesov, “Application of Conformal Mappings to Inequalities for Trigonometric Polynomials”, Mat. Zametki, 76:3 (2004), 396–408; Math. Notes, 76:3 (2004), 368–378

Citation in format AMSBIB
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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, “Schwarz's lemma and estimates of coefficients for regular functions with free domain of definition”, Sb. Math., 196:11 (2005), 1605–1625  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. 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  mathnet  elib
    3. V. N. Dubinin, S. I. Kalmukov, “On polynomials with constraints on circular arcs”, J. Math. Sci. (N. Y.), 184:6 (2012), 703–708  mathnet  crossref
    4. 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
    5. Nagy B., Totik V., “Bernstein's Inequality for Algebraic Polynomials on Circular Arcs”, Constr. Approx., 37:2 (2013), 223–232  crossref  mathscinet  zmath  isi  scopus  scopus
    6. 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
    7. L. S. Maergoiz, N. N. Rybakova, “Chebyshev polynomials with zeros on a circle and adjacent problems”, St. Petersburg Math. J., 25:6 (2014), 965–979  mathnet  crossref  mathscinet  zmath  isi  elib
    8. A. V. Olesov, “Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials”, Sb. Math., 205:10 (2014), 1413–1441  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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