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Zap. Nauchn. Sem. POMI, 2015, Volume 440, Pages 162–169 (Mi znsl6219)  

This article is cited in 1 scientific paper (total in 1 paper)

Polarization and circular truncation of a domain

V. O. Kuznetsov

Admiral Makarov State University of Maritime and Inland Shipping, St. Petersburg, Russia

Abstract: Difference of the reduced module $m(D)$ of a simply connected domain $D$ with respect to $z=0$ and the reduced module $m(D_r)$ of its circular truncation, where $D_r$ is the connected component of the set $D\cap\{|z|<r\}$, containing the point $z=0$, is considered. It is proved that in the case of polarization and circular symmetrization of the domain $D$ this difference does not decrease.

Key words and phrases: reduced module, polarization, symmetrization, extremal metric, Green's function.

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English version:
Journal of Mathematical Sciences (New York), 2016, 217:1, 108–113

Bibliographic databases:

UDC: 517.54
Received: 05.11.2015

Citation: V. O. Kuznetsov, “Polarization and circular truncation of a domain”, Analytical theory of numbers and theory of functions. Part 30, Zap. Nauchn. Sem. POMI, 440, POMI, St. Petersburg, 2015, 162–169; J. Math. Sci. (N. Y.), 217:1 (2016), 108–113

Citation in format AMSBIB
\Bibitem{Kuz15}
\by V.~O.~Kuznetsov
\paper Polarization and circular truncation of a~domain
\inbook Analytical theory of numbers and theory of functions. Part~30
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 440
\pages 162--169
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6219}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3504465}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 217
\issue 1
\pages 108--113
\crossref{https://doi.org/10.1007/s10958-016-2959-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84978121156}


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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. O. Kuznetsov, “Inner radius, polarization and circular truncation of the set”, J. Math. Sci. (N. Y.), 222:5 (2017), 641–644  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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