Geodesic
Equilibrium measure and the distribution of zeros of extremal polynomials
Sbornik. Mathematics, Tome 53 (1986) no. 1, pp. 119-130 
A. A. Gonchar; E. A. Rakhmanov. Equilibrium measure and the distribution of zeros of extremal polynomials. Sbornik. Mathematics, Tome 53 (1986) no. 1, pp. 119-130. http://geodesic.mathdoc.fr/item/SM_1986_53_1_a5/
@article{SM_1986_53_1_a5,
     author = {A. A. Gonchar and E. A. Rakhmanov},
     title = {Equilibrium measure and the distribution of zeros of extremal polynomials},
     journal = {Sbornik. Mathematics},
     pages = {119--130},
     year = {1986},
     volume = {53},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_53_1_a5/}
}
TY  - JOUR
AU  - A. A. Gonchar
AU  - E. A. Rakhmanov
TI  - Equilibrium measure and the distribution of zeros of extremal polynomials
JO  - Sbornik. Mathematics
PY  - 1986
SP  - 119
EP  - 130
VL  - 53
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1986_53_1_a5/
LA  - en
ID  - SM_1986_53_1_a5
ER  - 
%0 Journal Article
%A A. A. Gonchar
%A E. A. Rakhmanov
%T Equilibrium measure and the distribution of zeros of extremal polynomials
%J Sbornik. Mathematics
%D 1986
%P 119-130
%V 53
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1986_53_1_a5/
%G en
%F SM_1986_53_1_a5

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

The authors prove a theorem which characterizes the limit distribution of the zeros of polynomials $P_n$, $n=1,2,\dots$, defined by one (for each $n$) extremal relation with a variable (depending on $n$) weight function. Bibliography: 9 titles.

[1] Gonchar A. A., Rakhmanov E. A., “O skhodimosti sovmestnykh approksimatsii Pade dlya sistem funktsii markovskogo tipa”, Tr. MIAN, 157 (1981), 31–48 | MR | Zbl

[2] Rakhmanov E. A., “Ob asimptoticheskikh svoistvakh mnogochlenov, ortogonalnykh na veschestvennoi osi”, Matem. sb., 119(161) (1982), 169–203 | MR

[3] Stahl H., Doctorial Thesis, Technical Universität Berlin, 1976 | Zbl

[4] Saff E. B., Varga R. S., “The sharpness of Lorentz's theorem on incomplete polynomials”, Trans. Amer. Math. Soc., 249 (1979), 163–186 | DOI | MR | Zbl

[5] Lachance M., Saff E. B., Varga R. S., “Inequalities for Polynomials with Prescribed Zero”, Math. Zeit., 168 (1979), 105–116 | DOI | MR | Zbl

[6] Saff E. B., Ullman I. L., Varga R. S., “Incomplete polynomials: an electrostatics approach”, Approximation Theory III, ed. E. W. Cheney, Academic Press, 1980, 769–782 | MR

[7] Ullman I. L., “Orthogonal polynomials, associated with an infinite interval”, Michigan Math. J., 27 (1980), 353–363 | DOI | MR | Zbl

[8] Nevai P., Dehesa I. S., “On asymptotic average properties of zerous of orthogonal polynomials”, SIAM J. Math. Anal., 10 (1979), 1184–1192 | DOI | MR | Zbl

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