Geodesic
On the asymptotics of the ratio of orthogonal polynomials and convergence of multipoint Padé approximants
Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 207-219 
G. L. Lopes. On the asymptotics of the ratio of orthogonal polynomials and convergence of multipoint Padé approximants. Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 207-219. http://geodesic.mathdoc.fr/item/SM_1987_56_1_a12/
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     title = {On the asymptotics of the ratio of orthogonal polynomials and convergence of multipoint {Pad\'e} approximants},
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     url = {http://geodesic.mathdoc.fr/item/SM_1987_56_1_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A theorem is proved on the asymptotics of the ratio of polynomials orthogonal with respect to varying weights (that depend on the degree of the polynomial). Bibliography: 10 titles.

[1] Gonchar A. A., “O skhodimosti approksimatsii Pade dlya nekotorykh klassov meromorfnykh funktsii”, Matem. sb., 97(139) (1975), 607–629 | Zbl

[2] Gonchar A. A., Lopes G., “O teoreme Markova dlya mnogotochechnykh approksimatsii Pade”, Matem. sb., 105(147) (1978), 512–524 | MR | Zbl

[3] Geronimus Ya. L., Mnogochleny, ortogonalnye na okruzhnosti i otrezke, Fizmatgiz, M., 1958 | Zbl

[4] Zigmund A, Trigonometricheskie ryady, t. 1, Mir, M, 1965 | MR

[5] Rakhmanov E. A., “Ob asimptotike otnosheniya ortogonalnykh mnogochlenov”, Matem. sb., 103(145) (1977), 237–252 | Zbl

[6] Rakhmanov E. A., “Ob asimptotike otnosheniya ortogonalnykh mnogochlenov. II”, Matem. sb., 118(160) (1982), 104–117 | MR | Zbl

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

[8] Uolsh D., Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi ploskosti, IL, M., 1961

[9] Guillermo Lopez L., Jesus Illan, “Sobre la convergencia de los aproximantes multipuntuales de Padé para funciones de tipo stiltyes”, Rev. C. Mat., III (1981), 43–66

[10] Mate A., Nevai P., Totik V., “Asymptotics for the ratio of Leading Coefficientes of Orthonormal Polynomials on the Unit Circle”, Constr. Appr., 1 (1985), 63–69 | DOI | MR | Zbl