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Mat. Sb., 2009, Volume 200, Number 10, Pages 25–38 (Mi msb7535)  

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

Quadratic forms involving Green's and Robin functions

V. N. Dubinin

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

Abstract: General inequalities for quadratic forms with coefficients depending on the values of Green's and Robin functions are obtained. These inequalities cover also the reduced moduli of strips and half-strips. Some applications of the results obtained to extremal partitioning problems and related questions of geometric function theory are discussed.
Bibliography: 29 titles.

Keywords: Green's function, Robin function, reduced moduli, extremal decompositions, covering theorems.

DOI: https://doi.org/10.4213/sm7535

Full text: PDF file (553 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:10, 1439–1452

Bibliographic databases:

UDC: 517.54
MSC: Primary 30C85, 30C99; Secondary 31A15, 30C25
Received: 05.02.2009

Citation: V. N. Dubinin, “Quadratic forms involving Green's and Robin functions”, Mat. Sb., 200:10 (2009), 25–38; Sb. Math., 200:10 (2009), 1439–1452

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. D. A. Kirillova, “Univalent functions without common values”, Russian Math. (Iz. VUZ), 54:9 (2010), 74–76  mathnet  crossref  mathscinet  elib
    2. V. N. Dubinin, D. A. Kirillova, “Nekotorye primeneniya ekstremalnykh razbienii v geometricheskoi teorii funktsii”, Dalnevost. matem. zhurn., 10:2 (2010), 130–152  mathnet  elib
    3. Bakhtin A.K., Targonskii A.L., “Generalized $(n,d)$-ray systems of points and inequalities for nonoverlapping domains and open sets”, Ukr. Math. J., 63:7 (2011), 999–1012  crossref  zmath  isi  scopus
    4. Begehr H., Vaitekhovich T., “Modified harmonic Robin function”, Complex Variables and Elliptic Equations, 58:4 (2013), 483–496  crossref  mathscinet  zmath  isi  scopus
    5. E. G. Prilepkina, “Transfinite diameter with respect to Neumann function”, J. Math. Sci. (N. Y.), 200:5 (2014), 605–613  mathnet  crossref
    6. 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
    7. V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892  mathnet  crossref  mathscinet  isi
    8. E. G. Prilepkina, “On quadratic forms generated by the Neumann functions”, J. Math. Sci. (N. Y.), 207:6 (2015), 909–922  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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