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

M. A. Lapik

Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 211-224

Résumé

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.

Détail

Keywords: logarithmic vector potential, extremal vector measure.

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