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 Keldysh Institute preprints: Year: Volume: Issue: Page: Find

 Keldysh Institute preprints, 2016, 110 (Mi ipmp2184)

On the vector potential theory problem with the Angelesco matrix

V. G. Lysov, D. N. Tulyakov

Abstract: The vector equilibrium problems for the logarithmic potential with the Angelesco matrix of interactions are considered. For the case of two arbitrary intervals the solutions in the class of alternating charges and in the class of non-negative measures are researched. It is shown that the solutions are expressed in terms of algebraic functions. It is found that for the problem in the class of charges the genus of the algebraic curve is equal to zero for any location of the intervals. The explicit formulas of the equilibrium charges are found. The explicit formulas of the equilibrium measures are found under certain restrictions on the location of the intervals.

Keywords: vector equilibrium problem, Angelesco matrix of interaction, extremal measure, logarithmic potential, multiple orthogonal polynomials, spectral curve uniformization.

 Funding Agency Grant Number Russian Science Foundation 14-21-00025

DOI: https://doi.org/10.20948/prepr-2016-110

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Document Type: Preprint
UDC: 517.53

Citation: V. G. Lysov, D. N. Tulyakov, “On the vector potential theory problem with the Angelesco matrix”, Keldysh Institute preprints, 2016, 110, 36 pp.

Citation in format AMSBIB
\Bibitem{LysTul16} \by V.~G.~Lysov, D.~N.~Tulyakov \paper On the vector potential theory problem with the Angelesco matrix \jour Keldysh Institute preprints \yr 2016 \papernumber 110 \totalpages 36 \mathnet{http://mi.mathnet.ru/ipmp2184} \crossref{https://doi.org/10.20948/prepr-2016-110}