Asymptotics of simultaneously orthogonal polynomials in the Angelesco case
Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 57-84
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Asymptotic formulas for polynomials determined by orthogonality relations are obtained. The weight functions are concentrated on disjoint intervals. Fugures: 2. Bibliography: 24 titles.
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A. I. Aptekarev. Asymptotics of simultaneously orthogonal polynomials in the Angelesco case. Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 57-84. http://geodesic.mathdoc.fr/item/SM_1989_64_1_a3/

[1] Segë G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[2] Angelesko M. A., “Sur deux extensions des fractions continues algebriques”, C. r., 168 (1919), 262

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

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

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

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

[7] Nuttal J., “Asymptotics of diagonal Hermite–Pade polynomials”, J. Appr. Theor., 42:4 (1984), 259–386 | MR

[8] Aptekarev A. I., Kalyagin V. A., Asimptotika kornya $n$ stepeni iz polinomov sovmestnoi ortogonalnosti i algebraicheskie funktsii, Preprint IPM No 60, IPM AN SSSR, M., 1986

[9] Stahl H., Asymptotics of Hermite–Pade Polynomials and Related Approximants. A Summary of Results, Reprinte D-1000, Berlin, 1987

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

[11] Nuttal J., Singh S. R., “Orthogonal polynomials and Pade approximants associated with a system of arces”, J. Appr. Theor., 21 (1977), 1–42 | DOI | MR | Zbl

[12] Baumel R. T., Gammel J. L., Nuttal J., “Asymptotic form of Hermite–Pade polynomials”, IMA J. Appl. Math., 27 (1981), 335–357 | DOI | MR | Zbl

[13] Nuttal J., “Hermite–Pade approximants to functions meromorfic on a Riemann surfase”, J. Appr. Theor., 32 (1981), 233–240 | DOI | Zbl

[14] Kalyagin V. A., “O sovmestnykh approksimatsiyakh Pade dvukh logarifmov”, Trudy 2-i Vsesoyuznoi shkoly po teorii priblizhenii, 2, SGU, Saratov, 1984, 127–130

[15] Sorokin V. N., “Skhodimost sovmestnykh approksimatsii Pade k funktsiyam Stiltesovskogo tipa”, Izv. vuzov. Matematika, 1987, no. 7, 48–56 | MR | Zbl

[16] Parusnikov V. I., “On the convergent of the multidimensional limitperiodical continued fraction”, Lect. Not. Math., 1237 (1987), 217–227 | DOI | MR | Zbl

[17] Aptekarev A. I, Kalyagin V. A., “Analytic properties of two-dimensional continued fraction expantions with periodical coefficients and their simultanious pade–Hermite approximant”, Lect. Not. Math., 1237 (1987), 145–160 | DOI | MR | Zbl

[18] Keldisch M., “Sur l'approximation en moyenne quadratique des fonctions analytiques”, Matem. sb., 5(47) (1939), 391–402

[19] Suetin P. K., “Osnovnye svoistva mnogochlenov ortogonalnykh po konturu”, UMN, 21:2 (1966), 41–88 | MR | Zbl

[20] Babenko K. I., Osnovy chislennogo analiza, Nauka, M., 1986 | MR

[21] Gonchar A. A., Rakhmanov E. A., “Ravnovesnaya mera i raspredelenie nulei ekstremalnykh mnogochlenov”, Matem. sb., 125 (1984), 117–128 | MR

[22] Lopes G. L., “Ob asimptotike otnosheniya ortogonalnykh mnogochlenov i skhodimosti mnogotochechnykh approksimatsii Pade”, Matem. sb., 128(170) (1985), 216–229 | MR

[23] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 1, Mir, M., 1977 | MR

[24] Aptekarev A. I., Asimptotika polinomov sovmestnoi ortogonalnosti i sistemy ekstremalnykh zadach dlya analiticheskikh funktsii, Preprint IPM. No 168, IPM AN SSSR, M., 1987 | MR