Constructive Solution of One Vector Equilibrium Problem

A. I. Bogolyubskii^a and V. G. Lysov^a^,*

^aFederal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia

Correspondence to: *e-mail: vlysov@mail.ru

Received 26 December, 2019

Abstract—We study a two-dimensional vector logarithmic-potential equilibrium problem with the Nikishin matrix of interaction. A constructive method for finding the supports of a vector equilibrium measure is given. The densities of the components of the equilibrium measure are expressed in terms of an algebraic function that is explicitly written out. The problem is motivated by the study of the convergence of the Frobenius–Padé and Hermite–Padé rational approximants.

Keywords: logarithmic potential, vector equilibrium problem, Nikishin matrix of interaction, equilibrium measure, Frobenius–Padé approximants, Hermite–Padé approximants

DOI: 10.1134/S1064562420020064