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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 392, Pages 74–83 (Mi znsl4579)  
This article is cited in 3 scientific papers (total in 3 papers)

On polynomials with constraints on circular arcs

V. N. Dubinin, S. I. Kalmukov

Far Eastern Federal University, Vladivostok, Russia
Full-text PDF (222 kB) Citations (3)
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Abstract: For polynomials with prescribed minimal and maximal values of their moduli on a collection of circular arcs it is shown that new covering and distortion theorems and a modulus estimates for a product of leading and free coefficients follow from a majorization principle for meromorphic functions proved by the authors earlier. As corollaries, recent results on polynomials with additional constraints on zeros established by other mathematicians are obtained.
Key words and phrases: covering and distortion theorems, inequalities for polynomials, Chebyshev polynomials, majorization principles.
Received: 05.05.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 184, Issue 6, Pages 703–708
DOI: https://doi.org/10.1007/s10958-012-0892-2
Bibliographic databases:
Document Type: Article
UDC: 512.62+517.54
Language: Russian
Citation: V. N. Dubinin, S. I. Kalmukov, “On polynomials with constraints on circular arcs”, Analytical theory of numbers and theory of functions. Part 26, Zap. Nauchn. Sem. POMI, 392, POMI, St. Petersburg, 2011, 74–83; J. Math. Sci. (N. Y.), 184:6 (2012), 703–708
Citation in format AMSBIB
\Bibitem{DubKal11}
\by V.~N.~Dubinin, S.~I.~Kalmukov
\paper On polynomials with constraints on circular arcs
\inbook Analytical theory of numbers and theory of functions. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 392
\pages 74--83
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4579}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 184
\issue 6
\pages 703--708
\crossref{https://doi.org/10.1007/s10958-012-0892-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864287699}
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  • https://www.mathnet.ru/eng/znsl/v392/p74
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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