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Zap. Nauchn. Sem. POMI, 2004, Volume 314, Pages 52–75 (Mi znsl749)  

This article is cited in 13 scientific papers (total in 13 papers)

Some applications of generalized condensers to analytic function theory

V. N. Dubinin, N. V. Eyrikh

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

Abstract: New applications of generalized condensers with two or more plates are considered. Based on one and the same approach and simplest properties of such condensers, boundary distortion theorems for analytic univalent functions bounded in a disk are established, as well as bounds for certain combinations of coefficients in expansions of such functions, inequalities for polynomials, and theorems on extremal decompositions of the complex sphere. Part of the results obtained contains new information on the Schwarzian derivative of a regular univalent function.

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English version:
Journal of Mathematical Sciences (New York), 2006, 133:6, 1634–1647

Bibliographic databases:

UDC: 517.54
Received: 19.08.2004

Citation: V. N. Dubinin, N. V. Eyrikh, “Some applications of generalized condensers to analytic function theory”, Analytical theory of numbers and theory of functions. Part 20, Zap. Nauchn. Sem. POMI, 314, POMI, St. Petersburg, 2004, 52–75; J. Math. Sci. (N. Y.), 133:6 (2006), 1634–1647

Citation in format AMSBIB
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\by V.~N.~Dubinin, N.~V.~Eyrikh
\paper Some applications of generalized condensers to analytic function theory
\inbook Analytical theory of numbers and theory of functions. Part~20
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 314
\pages 52--75
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl749}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2119734}
\zmath{https://zbmath.org/?q=an:1083.30026}
\elib{http://elibrary.ru/item.asp?id=9129779}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 133
\issue 6
\pages 1634--1647
\crossref{https://doi.org/10.1007/s10958-006-0076-z}
\elib{http://elibrary.ru/item.asp?id=13511170}


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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, E. G. Prilepkina, “O sokhranenii obobschennogo privedennogo modulya pri geometricheskikh preobrazovaniyakh ploskikh oblastei”, Dalnevost. matem. zhurn., 6:1-2 (2005), 39–56  mathnet  elib
    3. V. N. Dubinin, “Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization”, J. Math. Sci. (N. Y.), 143:3 (2007), 3053–3068  mathnet  crossref  mathscinet  zmath  elib  elib
    4. V. N. Dubinin, E. G. Prilepkina, “On variational principles of conformal mappings”, St. Petersburg Math. J., 18:3 (2007), 373–389  mathnet  crossref  mathscinet  zmath  elib
    5. E. G. Emel'yanov, “On quadratic differentials in multiply connected domains that are perfect squares. II”, J. Math. Sci. (N. Y.), 150:3 (2008), 2027–2033  mathnet  crossref
    6. Karp D., Prilepkina E., “Reduced modulus with free boundary and its applications”, Ann. Acad. Sci. Fenn. Math., 34:2 (2009), 353–378  mathscinet  zmath  isi  elib
    7. V. N. Dubinin, E. G. Prilepkina, “Distortion theorems for univalent meromorphic functions on an annulus”, Siberian Math. J., 51:2 (2010), 229–243  mathnet  crossref  mathscinet  isi  elib  elib
    8. V. N. Dubinin, D. A. Kirillova, “Nekotorye primeneniya ekstremalnykh razbienii v geometricheskoi teorii funktsii”, Dalnevost. matem. zhurn., 10:2 (2010), 130–152  mathnet  elib
    9. E. G. Prilepkina, “On composition principles for reduced moduli”, Siberian Math. J., 52:6 (2011), 1079–1091  mathnet  crossref  mathscinet  isi
    10. V. N. Dubinin, V. Yu. Kim, “Obobschennye kondensatory i teoremy o granichnom iskazhenii pri konformnom otobrazhenii”, Dalnevost. matem. zhurn., 13:2 (2013), 196–208  mathnet
    11. V. N. Dubinin, “Asymptotic Behavior of the Capacity of a Condenser as Some of Its Plates Contract to Points”, Math. Notes, 96:2 (2014), 187–198  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892  mathnet  crossref  mathscinet  isi
    13. V. N. Dubinin, “Geometric estimates for the Schwarzian derivative”, Russian Math. Surveys, 72:3 (2017), 479–511  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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