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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.”

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
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