Geodesic
Strong asymptotics of multiply orthogonal polynomials for Nikishin systems
Sbornik. Mathematics, Tome 190 (1999) no. 5, pp. 631-669 Cet article a éte moissonné depuis la source Math-Net.Ru

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Strong asymptotic formulae for the Hermite–Padé polynomials for systems of Markov-type functions in the Nikishin class are obtained. The proof is based on the properties of certain rational functions on Riemann surfaces associated with the supports of the measures generating the Nikishin system. 
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A. I. Aptekarev. Strong asymptotics of multiply orthogonal polynomials for Nikishin systems. Sbornik. Mathematics, Tome 190 (1999) no. 5, pp. 631-669. http://geodesic.mathdoc.fr/item/SM_1999_190_5_a0/

[1] Nikishin E. M., “Sovmestnye approksimatsii Pade”, Matem. sb., 113 (155):4 (12) (1980), 499–519 | MR | Zbl

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

[3] Angelesco A., “Sur l'approximation simultanée des plusieurs intégrales définies”, C. R. Acad. Sci. Paris. Sér. I Math., 167 (1918), 629–631

[4] Nikishin E. M., “O sisteme markovskikh funktsii”, Vestn. MGU. Ser. 1. Matem., mekh., 1979, no. 4, 60–63 | MR | Zbl

[5] Aptekarev A. I., Marcellán F., Rocha I. A., “Semiclassical multiple ortogonal polynomials and the properties of Jacobi–Bessel polynomials”, J. Approx. Theory, 90 (1997), 117–146 | DOI | MR | Zbl

[6] Aptekarev A., Stahl H., “Asymptotics of Hermite–Padé polynomials”, Progress in Approximation Theory, eds. A. Gonchar, E. B. Saff, Springer-Verlag, Berlin, 1992, 127–167 | MR | Zbl

[7] Nuttall J., “Asymptotics of diagonal Hermite–Padé polynomials”, J. Approx. Theory, 42 (1984), 299–386 | DOI | MR | Zbl

[8] Kalyagin V. A., “O klasse polinomov, opredelennykh dvumya sootnosheniyami ortogonalnosti”, Matem. sb., 110 (152):4 (12) (1979), 609–627 | MR

[9] Bernstein S. N., “Sur les polynomes orthogonaux relatifs à un segment fini. I; II”, J. Math. Pures Appl., 9 (1930), 127–177 ; J. Math. Pures Appl., 10 (1931), 219–286 | Zbl | Zbl

[10] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[11] Aptekarev A. I., “Asimptotika polinomov sovmestnoi ortogonalnosti v sluchae Andzhelesko”, Matem. sb., 136 (178):1 (5) (1988), 56–84 | MR

[12] Gonchar A. A., Rakhmanov E. A., “Skhodimost sovmestnykh approksimatsii Pade dlya sistemy markovskikh funktsii”, Tr. MIAN, 157, Nauka, M., 1981, 31–48 | MR | Zbl

[13] Nikishin E. M., “Asimptotika lineinykh form dlya sovmestnykh approksimatsii Pade”, Izv. vuzov. Ser. matem., 1986, no. 2, 33–41 | MR | Zbl

[14] Bustamante Zh., Lopes G. Lagomasino, “Approksimatsii Ermita–Pade dlya sistem Nikishina analiticheskikh funktsii”, Matem. sb., 183:11 (1992), 117–138 | MR | Zbl

[15] Driver K., Stahl H., “Normality in Nikishin systems”, Indag. Math. (N.S.), 5:2 (1994), 161–187 | DOI | MR | Zbl

[16] Driver K., Stahl H., “Simultaneons rational approximants to Nikishin systems, I”, Acta Sci. Math., 60 (1995), 245–263 | MR | Zbl

[17] Driver K., Stahl H., “Simultaneus rational approximants to Nikishin systems, II”, Acta Sci. Math., 61 (1995), 261–284 | MR | Zbl

[18] Stahl H., “Simultaneous rational approximants”, Computational methods and function theory, 1994, Proceedings of the conference (Penang, Malaysia, March 21–25, 1994), eds. Ali R. M. et al., World Scientific, Singapore, 1995, 325–349 | MR | Zbl

[19] López Lagomasino G., “Asymptotics of polynomials orthogonal with respect to varying measures”, Constr. Approx., 5 (1989), 199–219 | DOI | MR | Zbl

[20] Lopes G., “Ob asimptotike otnosheniya ortogonalnykh mnogochlenov i skhodimosti mnogotochechnykh approksimatsii Pade”, Matem. sb., 128 (170):2 (1985), 216–228 | MR

[21] de la Calle Y. B., López L. G., “Weak convergence of varying measures and Hermite–Padé orthogonal polynomials”, Constr. Approx., 15:4 (1999) | MR

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

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