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 Tr. Mat. Inst. Steklova, 2018, Volume 301, Pages 192–208 (Mi tm3914)

On the supports of vector equilibrium measures in the Angelesco problem with nested intervals

V. G. Lysovab, D. N. Tulyakova

a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia
b Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia

Abstract: A vector logarithmic-potential equilibrium problem with the Angelesco interaction matrix is considered for two nested intervals with a common endpoint. The ratio of the lengths of the intervals is a parameter of the problem, and another parameter is the ratio of the masses of the components of the vector equilibrium measure. Two cases are distinguished, depending on the relations between the parameters. In the first case, the equilibrium measure is described by a meromorphic function on a three-sheeted Riemann surface of genus zero, and the supports of the components do not overlap and are connected. In the second case, a solution to the equilibrium problem is found in terms of a meromorphic function on a six-sheeted surface of genus one, and the supports overlap and are not connected.

 Funding Agency Grant Number Russian Science Foundation 14-21-00025 This work is supported by the Russian Science Foundation under grant 14-21-00025.

DOI: https://doi.org/10.1134/S0371968518020140

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 301, 180–196

Bibliographic databases:

UDC: 517.53

Citation: V. G. Lysov, D. N. Tulyakov, “On the supports of vector equilibrium measures in the Angelesco problem with nested intervals”, Complex analysis, mathematical physics, and applications, Collected papers, Tr. Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 192–208; Proc. Steklov Inst. Math., 301 (2018), 180–196

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3914
• https://doi.org/10.1134/S0371968518020140
• http://mi.mathnet.ru/eng/tm/v301/p192

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This publication is cited in the following articles:
1. A. I. Aptekarev, R. Kozhan, “Differential equations for the radial limits in $\mathbb{Z}_+^2$ of the solutions of a discrete integrable system”, Preprinty IPM im. M. V. Keldysha, 2018, 214, 20 pp.
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