Geodesic
Hermite–Pade approximants for systems of Markov-type functions
Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 671-696 
A. A. Gonchar; E. A. Rakhmanov; V. N. Sorokin. Hermite–Pade approximants for systems of Markov-type functions. Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 671-696. http://geodesic.mathdoc.fr/item/SM_1997_188_5_a2/
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     author = {A. A. Gonchar and E. A. Rakhmanov and V. N. Sorokin},
     title = {Hermite{\textendash}Pade approximants for systems of {Markov-type} functions},
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     volume = {188},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_5_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Hermite–Pade approximants are studied for systems of Markov functions (introduced in this paper) with structure described by a graph. Results of an asymptotic nature are stated in terms of certain equilibrium problems of potential theory concerning vector potentials.

[1] Hermite C., “Sur la fonction exponentielle”, C. R. Acad. Sci. Paris Sér. I Math., 77 (1873), 18–24; 74–79 ; 226–233 ; 285–293 | Zbl

[2] Mahler K., “Perfect systems”, Compositio Math., 19:2 (1968), 95–166 | MR | Zbl

[3] Nuttall J., “Asymptotics of diagonal Hermite–Padé polynomials”, J. Approx. Theory, 42 (4) (1984), 259–386 | DOI | MR

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

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

[6] Kalyagin V. A., “Ob odnom klasse polinomov, opredelyaemykh dvumya sootnosheniyami ortogonalnosti”, Matem. sb., 110 (152) (1979), 609–627 | MR

[7] Gonchar A. A., Rakhmanov E. A., “O skhodimosti sovmestnykh approksimatsii Pade dlya sistemy funktsii markovskogo tipa”, Tr. MIAN, 157, Nauka, M., 1981, 31–48 | MR | Zbl

[8] Aptekarev A. I., “Asimptotika mnogochlenov sovmestnoi ortogonalnosti v sluchae Anzhelesko”, Matem. sb., 136 (1988), 56–84 | MR

[9] Nikishin E. M., “O sovmestnykh approksimatsiyakh Pade”, Matem. sb., 113 (155):4 (1980), 499–519 | MR | Zbl

[10] Nikishin E. M., “Ob asimptotike lineinykh form dlya sovmestnykh approksimatsii Pade”, Izv. vuzov. Matem., 1986, no. 2, 33–41 | MR | Zbl

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

[12] Sorokin V. N., “Approksimatsii Ermita–Pade polilogarifmov”, Izv. vuzov. Matem., 1994, no. 5, 49–59 | MR | Zbl

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

[14] Bustamante J., “Asymptotics for Angelesco–Nikishin Systems”, J. Approx. Theory, 85 (1996), 43–68 | DOI | MR | Zbl

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

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

[17] Gonchar A. A., Rakhmanov E. A., “Ravnovesnye raspredeleniya i skorost ratsionalnoi approksimatsii analiticheskikh funktsii”, Matem. sb., 134 (176) (1987), 306–352 | MR | Zbl