Convergence of padÉ approximants of stieltjes type meromorphic functions and comparative asymptotics for orthogonal polynomials

Mathematics of the USSR - Sbornik

Volumn 64, Issue 1, 1989, Pages 207-227

  Lopes, G L ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

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[No Author keywords available]

Indexed keywords

EID: 0000679057     PISSN: 00255734     EISSN: 21695288     Source Type: Journal    
DOI: 10.1070/SM1989v064n01ABEH003303     Document Type: Article

References (13)

1. T. J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sei. Univ. Toulouse 8 (1894), Vol Jl-J122; 9 (1895), A1-A47.
2. Torsten Carleman, Les fonctions quasi analytiques, Gauthier-Villars, Paris, 1926.
3. G. Lopes [G. Löpez L.], On the convergence of Padé approximants for meromorphic functions of Stieltjes type, Mat. Sb. 111(153) (1980), 308-316; English transl. in Math. USSR Sb. 39 (1981) 281-288.
4. A. A. Gonchar, On the convergence of Padé approximants for some classes of meromorphic functions, Mat. Sb. 97(139) (1975), 607-629; English transl. in Math. USSR Sb. 26 (1975)
5. E. A. Rakhmanov, On the asymptotics of the ratio of orthogonal polynomials, Mat. Sb. 103(145) (1977), 237-252; English transl. in Math. USSR Sb. 32 (1977).
6. E. A. Rakhmanov, On the asymptotics of the ratio of orthogonal polynomials. II, Mat. Sb. 118(160) (1982), 104-117; English transl. in Math. USSR Sb. 46 (1983).
7. G. Lopes [G. Löpez L.], On the asymptotics of the ratio of orthogonal polynomials and convergence of multipoint Padé approximants, Mat. Sb. 128(170) (1985), 216-229; English transl. in Math. USSR Sb. 56 (1987).
8. Attila Mäté, Paul Nevai, and Vilmos Totik, Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle, Constructive Approximation 1 (1985), 63-69.
9. G. M. Goluzin, Geometric theory of functions of a complex variable, 2nd ed., “Nauka”, Moscow, 1966; English transl., Amer. Math. Soc., Providence, R.I., 1969.
10. A. A. Gonchar, On the convergence of generalized Padé approximants of meromorphic functions, Mat. Sb. 98(140) (1975), 564-577; English transl. in Math. USSR Sb. 27 (1975).
11. Ya. L. Geronimus, Polynomials orthogonal on the unit circle and on an interval, Fizmatgiz, Moscow, 1958; English transl., Orthogonal polynomials, Consultants Bureau, New York, 1961.
12. G. Lopes [G. Löpez L.], Conditions for convergence of multipoint Padé approximants for functions of Stieltjes type, Mat. Sb. 107(149) (1978), 69-83; English transl. in Math. USSR Sb. 35 (1979), no. 3.
13. J. L. Walsh, Introduction and approximation by rational functions in the complex domain, 2nd ed., Amer. Math. Soc., Providence, R.I., 1956.