Geodesic
Multipoint Hermite--Pad\'e approximants for three beta functions
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 79 (2018) no. 1, pp. 133-153.

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This paper is concerned with joint multipoint rational approximants with a common denominator for three beta functions. The limit distributions of the zeros of the denominators are obtained in terms of equilibrium logarithmic potentials and in terms of meromorphic functions on Riemann surfaces. 
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V. N. Sorokin. Multipoint Hermite--Pad\'e approximants for three beta functions. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 79 (2018) no. 1, pp. 133-153. http://geodesic.mathdoc.fr/item/MMO_2018_79_1_a3/

[1] Kandayan A. A., “Mnogotochechnye approksimatsii Pade beta-funktsii”, Matem. zametki, 85:2 (2009), 189–203 | DOI | Zbl

[2] Kandayan A. A., Sorokin V. N., “Mnogotochechnye approksimatsii Ermita–Pade beta-funktsii”, Matem. zametki, 87:2 (2010), 217–232 | DOI | Zbl

[3] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966

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

[5] Sorokin V. N., “O mnogochlenakh sovmestnoi ortogonalnosti dlya diskretnykh mer Meiksnera”, Matem. sb., 201:10 (2010), 137–160 | DOI

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

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

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

[9] Rakhmanov E. A., “Ravnovesnaya mera i raspredelenie nulei ekstremalnykh mnogochlenov diskretnoi peremennoi”, Matem. sb., 187:8 (1996), 109–124 | DOI | Zbl

[10] Gonchar A. A., Rakhmanov E. A., Suetin S. P., “Approksimatsii Pade–Chebyshëva dlya mnogoznachnykh analiticheskikh funktsii, variatsiya ravnovesnoi energii i S-svoistvo statsionarnykh kompaktov”, UMN, 66:6 (2011), 3–36 | DOI

[11] Martines-Filkenshtein A., Rakhmanov E. A., Suetin S. P., “Variatsiya ravnovesnoi energii i S-svoistvo statsionarnogo kompakta”, Matem. sb., 202:12 (2011), 113–136 | DOI | Zbl

[12] Nikishin E. M., “O sovmestnykh approksimatsiyakh Pade”, Matem. sb., 113(145):4 (1980), 499–519 | Zbl

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

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