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Equilibrium measure for the vector logarithmic potential problem with an external field and the Nikishin interaction matrix. (English. Russian original) Zbl 1253.31003
Russ. Math. Surv. 67, No. 3, 579-581 (2012); translation from Usp. Mat. Nauk. 67, No. 3, 179-180 (2012).
From the text: “Families (with respect to $$x$$) of scalar extremal measures in an external field were first considered by V. S. Buyarov and E. A. Rakhmanov [Sb. Math. 190, No. 6, 791–802 (1999); translation from Mat. Sb. 190, No. 6, 11–22 (1999; Zbl 0933.31002)]. In general we are following their approach extending it to the vector case. In [Sb. Math. 197, No. 8, 1205–1221 (2006); translation from Mat. Sb. 197, No. 8, 101–118 (2006; Zbl 1148.31005)] the author showed that vector extremal measures increase with respect to the total mass parameter $$x$$. Here we give explicit formulae for extremal measures.”

##### MSC:
 31A10 Integral representations, integral operators, integral equations methods in two dimensions 31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
##### Keywords:
extremal measures
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