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Zap. Nauchn. Sem. POMI, 2006, Volume 337, Pages 101–112 (Mi znsl184)  

This article is cited in 7 scientific papers (total in 7 papers)

Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros

V. N. Dubinin

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

Abstract: It is shown that new inequalities for certain classes of entire functions can be obtained by applying the Schwarz lemma and its generalizations to specially constructed Blaschke products. In particular, for entire functions of exponential type whose zeros lie in the closed lower half-plane, distortion theorems, including the two-point distortion theorem on the real axis, are proved. Similar results are established for polynomials with zeros in the closed unit disk. The classical theorems by Turan and Ankeny–Rivlin are refined. In addition, a theorem on the mutual disposition of the zeros and critical points of a polynomial is proved. Bibliography: 16 titles.

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English version:
Journal of Mathematical Sciences (New York), 2007, 143:3, 3069–3076

Bibliographic databases:

UDC: 517.54
Received: 04.05.2006

Citation: V. N. Dubinin, “Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros”, Analytical theory of numbers and theory of functions. Part 21, Zap. Nauchn. Sem. POMI, 337, POMI, St. Petersburg, 2006, 101–112; J. Math. Sci. (N. Y.), 143:3 (2007), 3069–3076

Citation in format AMSBIB
\Bibitem{Dub06}
\by V.~N.~Dubinin
\paper Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros
\inbook Analytical theory of numbers and theory of functions. Part~21
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 337
\pages 101--112
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl184}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2271959}
\zmath{https://zbmath.org/?q=an:1117.30016}
\elib{http://elibrary.ru/item.asp?id=9305276}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 3
\pages 3069--3076
\crossref{https://doi.org/10.1007/s10958-007-0192-4}
\elib{http://elibrary.ru/item.asp?id=13546865}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248139007}


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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, D. B. Karp, V. A. Shlyk, “Izbrannye zadachi geometricheskoi teorii funktsii i teorii potentsiala”, Dalnevost. matem. zhurn., 8:1 (2008), 46–95  mathnet  elib
    2. V. V. Vasin, V. N. Dubinin, V. G. Romanov, “Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke””, Sib. elektron. matem. izv., 5 (2008), 427–439  mathnet  elib
    3. V. N. Dubinin, “Emkosti kondensatorov i printsipy mazhoratsii v geometricheskoi teorii funktsii kompleksnogo peremennogo [Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke”]”, Sib. elektron. matem. izv., 5 (2008), 465–482  mathnet  mathscinet
    4. A. V. Olesov, “Differential inequalities for algebraic polynomials”, Siberian Math. J., 51:4 (2010), 706–711  mathnet  crossref  mathscinet  isi
    5. 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
    6. S. I. Kalmykov, “Neravenstva dlya modulei ratsionalnykh funktsii”, Dalnevost. matem. zhurn., 12:2 (2012), 231–236  mathnet
    7. Azeroglu T.A. Ornek B.N., “A Refined Schwarz Inequality on the Boundary”, Complex Var. Elliptic Equ., 58:4, SI (2013), 571–577  crossref  mathscinet  zmath  isi  elib  scopus
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