This article is cited in 15 papers

Families of vector measures which are equilibrium measures in an external field

M. A. Lapik

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow

Abstract: We consider vector extremal problems in the theory of logarithmic potential with external field by looking at an example of two-dimensional problems with Nikishin interaction matrix and variable masses $2x$ and $x$ of the first and second components of the vector measure, respectively. The dependence of the supports of the equilibrium measures, equlibrium constants and energy on the parameter $x$ is analysed. Integral formulae recovering the extremal measure with mass $x$ from the supports of extremal measures with smaller masses are obtained.
Bibliography: 27 titles.

Keywords: logarithmic vector potential, extremal vector measure.

UDC: 517.53

MSC: 31A10, 31A15

Received: 17.02.2014 and 08.12.2014

DOI: 10.4213/sm8347

 English version: Sbornik: Mathematics, 2015, 206:2, 211–224

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