Geodesic
Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable
Sbornik. Mathematics, Tome 187 (1996) no. 8, pp. 1213-1228 
E. A. Rakhmanov. Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable. Sbornik. Mathematics, Tome 187 (1996) no. 8, pp. 1213-1228. http://geodesic.mathdoc.fr/item/SM_1996_187_8_a3/
@article{SM_1996_187_8_a3,
     author = {E. A. Rakhmanov},
     title = {Equilibrium measure and the~distribution of zeros of the~extremal polynomials of a~discrete variable},
     journal = {Sbornik. Mathematics},
     pages = {1213--1228},
     year = {1996},
     volume = {187},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_8_a3/}
}
TY  - JOUR
AU  - E. A. Rakhmanov
TI  - Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 1213
EP  - 1228
VL  - 187
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_8_a3/
LA  - en
ID  - SM_1996_187_8_a3
ER  - 
%0 Journal Article
%A E. A. Rakhmanov
%T Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable
%J Sbornik. Mathematics
%D 1996
%P 1213-1228
%V 187
%N 8
%U http://geodesic.mathdoc.fr/item/SM_1996_187_8_a3/
%G en
%F SM_1996_187_8_a3

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

The problem of the limiting distribution of the zeros of the polynomial extremal in the $L^2$-metric with respect to a measure with finitely many points of growth is studied under the assumption that the degree $n$ of this polynomial and the number $N$ ($N>n$) of points of growth of the measure approach infinity so that $n/N\to c\in (0,1)$.

[1] Chebyshev P. L., “Ob interpolirovanii velichin ravnootstoyaschikh”, Polnoe sobranie sochinenii, Izd-vo AN SSSR, M.–L., 1948 | MR

[2] Nikiforov A. F., Suslov S. K., Uvarov V. B., Klassicheskie ortogonalnye mnogochleny diskretnoi peremennoi, Nauka, M., 1985 | MR

[3] Sharapudinov I. I., “Asimptoticheskie svoistva ortogonalnykh mnogochlenov Khana diskretnoi peremennoi”, Matem. sb., 180:9 (1989), 1259–1277 | MR | Zbl

[4] Gonchar A. A., Rakhmanov E. A., “Ravnovesnaya mera i raspredelenie nulei ekstremalnykh mnogochlenov”, Matem. sb., 125 (1984), 117–127 | MR

[5] Saff E. B., Totik V., Logarithmic Potentials with external Fields, Springer-Verlag, New York (to appear) | MR

[6] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl