Geodesic
On a Vector Potential-Theory Equilibrium Problem with the Angelesco Matrix
Informatics and Automation, Complex analysis and its applications, Tome 298 (2017), pp. 185-215

Voir la notice de l'article provenant de la source Math-Net.Ru

Vector logarithmic-potential equilibrium problems with the Angelesco interaction matrix are considered. Solutions to two-dimensional problems in the class of measures and in the class of charges are studied. It is proved that in the case of two arbitrary real intervals, a solution to the problem in the class of charges exists and is unique. The Cauchy transforms of the components of the equilibrium charge are algebraic functions whose degree can take values $2$, $3$, $4$, and $6$ depending on the arrangement of the intervals. A constructive method for finding the vector equilibrium charge in an explicit form is presented, which is based on the uniformization of an algebraic curve. An explicit form of the vector equilibrium measure is found under some constraints on the arrangement of the intervals.
Keywords: vector equilibrium problem, Angelesco interaction matrix, logarithmic potential, extremal measure, algebraic functions, uniformization of an algebraic curve. 
@article{TRSPY_2017_298_a12,
     author = {V. G. Lysov and D. N. Tulyakov},
     title = {On a {Vector} {Potential-Theory} {Equilibrium} {Problem} with the {Angelesco} {Matrix}},
     journal = {Informatics and Automation},
     pages = {185--215},
     publisher = {mathdoc},
     volume = {298},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a12/}
}
TY  - JOUR
AU  - V. G. Lysov
AU  - D. N. Tulyakov
TI  - On a Vector Potential-Theory Equilibrium Problem with the Angelesco Matrix
JO  - Informatics and Automation
PY  - 2017
SP  - 185
EP  - 215
VL  - 298
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a12/
LA  - ru
ID  - TRSPY_2017_298_a12
ER  - 
%0 Journal Article
%A V. G. Lysov
%A D. N. Tulyakov
%T On a Vector Potential-Theory Equilibrium Problem with the Angelesco Matrix
%J Informatics and Automation
%D 2017
%P 185-215
%V 298
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a12/
%G ru
%F TRSPY_2017_298_a12
V. G. Lysov; D. N. Tulyakov. On a Vector Potential-Theory Equilibrium Problem with the Angelesco Matrix. Informatics and Automation, Complex analysis and its applications, Tome 298 (2017), pp. 185-215. http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a12/