Geodesic
Support of the extremal measure in a vector equilibrium
Sbornik. Mathematics, Tome 197 (2006) no. 8, pp. 1205-1221 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A generalization of the Mhaskar–Saff functional is obtained for a vector equilibrium problem with an external field. As an application, the supports of the equilibrium measures are found in a special vector equilibrium problem with Nikishin matrix. Bibliography: 13 titles. 
@article{SM_2006_197_8_a5,
     author = {M. A. Lapik},
     title = {Support of the extremal measure in a vector equilibrium},
     journal = {Sbornik. Mathematics},
     pages = {1205--1221},
     year = {2006},
     volume = {197},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_8_a5/}
}
TY  - JOUR
AU  - M. A. Lapik
TI  - Support of the extremal measure in a vector equilibrium
JO  - Sbornik. Mathematics
PY  - 2006
SP  - 1205
EP  - 1221
VL  - 197
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_2006_197_8_a5/
LA  - en
ID  - SM_2006_197_8_a5
ER  - 
%0 Journal Article
%A M. A. Lapik
%T Support of the extremal measure in a vector equilibrium
%J Sbornik. Mathematics
%D 2006
%P 1205-1221
%V 197
%N 8
%U http://geodesic.mathdoc.fr/item/SM_2006_197_8_a5/
%G en
%F SM_2006_197_8_a5
M. A. Lapik. Support of the extremal measure in a vector equilibrium. Sbornik. Mathematics, Tome 197 (2006) no. 8, pp. 1205-1221. http://geodesic.mathdoc.fr/item/SM_2006_197_8_a5/

[1] A. A. Gonchar, E. A. Rakhmanov, “Ravnovesnaya mera i raspredelenie nulei ekstremalnykh mnogochlenov”, Matem. sb., 125(167):1 (1984), 117–127 | MR | Zbl

[2] E. M. Nikishin, V. N. Sorokin, Ratsionalnye approksimatsii i ortogonalnost, Nauka, Fizmatlit, M., 1988 | MR | Zbl

[3] E. B. Saff, V. Totik, Logarithmic potentials with external fields, Grundlehren Math. Wiss., 316, Springer-Verlag, Berlin, 1997 | MR | Zbl

[4] A. I. Aptekarev, W. Van Assche, “Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice”, J. Phys. A, 34 (2001), 10627–10637 | DOI | MR | Zbl

[5] P. Deift, K. T.-R. McLaughlin, A continuum limit of the Toda lattice, Mem. Amer. Math. Soc., 624, Amer. Math. Soc., Providence, RI, 1998 | MR | Zbl

[6] A. B. J. Kuijlaars, W. Van Assche, “A contact problem in elasticity related to weighted polynomials on the real line”, Proceedings of the Third International Conference on Functional Analysis and Approximation Theory, vol. II (Italy, September 23–28, 1996), Circolo Matematico di Palermo, Palermo, 1998, 575–587 | MR | Zbl

[7] A. A. Gonchar, E. A. Rakhmanov, “O skhodimosti sovmestnykh approksimatsii Pade dlya sistem funktsii markovskogo tipa”, Teoriya chisel, matematicheskii analiz i ikh prilozheniya, Tr. MIAN, 157, 1981, 31–48 | MR | Zbl

[8] A. A. Gonchar, E. A. Rakhmanov, “O zadache ravnovesiya dlya vektornykh potentsialov”, UMN, 40:4 (1985), 155–156 | MR | Zbl

[9] A. A. Gonchar, E. A. Rakhmanov, V. N. Sorokin, “Ob approksimatsiyakh Ermita–Pade dlya sistem funktsii markovskogo tipa”, Matem. sb., 188:5 (1997), 33–58 | MR | Zbl

[10] H. N. Mhaskar, E. B. Saff, “Where does the sup norm of a weighted polynomial live? A generalization of incomplete polynomials”, Constr. Approx., 1 (1985), 71–91 | DOI | MR | Zbl

[11] V. S. Buyarov, E. A. Rakhmanov, “O semeistvakh mer, ravnovesnykh vo vneshnem pole na veschestvennoi osi”, Matem. sb., 190:6 (1999), 11–22 | MR | Zbl

[12] A. I. Aptekarev, “Silnaya asimptotika mnogochlenov sovmestnoi ortogonalnosti dlya sistem Nikishina”, Matem. sb., 190:5 (1999), 3–44 | MR | Zbl

[13] H. Widom, “Extremal polynomials associated with a system of curves in the complex plane”, Adv. Math., 3 (1969), 127–232 | DOI | MR | Zbl