On the asymptotics of the ratio of orthogonal polynomials and convergence of multipoint padÉ approximants

Mathematics of the USSR - Sbornik

Volumn 56, Issue 1, 1987, Pages 207-219

  Lopes, G L ^a  

^a NONE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039857091     PISSN: 00255734     EISSN: 21695288     Source Type: Journal    
DOI: 10.1070/SM1987v056n01ABEH003032     Document Type: Article

References (15)

1. A. Gonchar, On convergence of Pade approximants for some classes of meromorphic functions, Mat. Sb. 97(139) (1975), 607-629.
2. A. A. Gonchar, English transl. in Math. USSR Sb. 26 (1975).
3. A. A. Gonchar and G. Lopes, On Markov’s theorem for multipoint Pade approximants, Mat. Sb. 105(147) (1978), 512-524.
4. A. A. Gonchar and G. Lopes, English transl. in Math. USSR Sb. 34 (1978).
5. Ya. L. Geronimus, Polynomials orthogonal on a circumference and on an interval, Fizmatgiz, Moscow, 1958.
6. Ya. L. Geronimus, English transl., Orthogonal polynomials, Consultants Bureau, New York, 1961.
7. A. Zygmund, Trigonometric series, 2nd rev. ed., Vol. 1, Cambridge Univ. Press, 1959.
8. E. A. Rakhmanov, On the asymptotics of the ratio of orthogonal polynomials, Mat. Sb. 103(145) (1977), 237-252.
9. E. A. Rakhmanov, English transl. in Math USSR Sb. 32 (1977).
10. E. A. Rakhmanov, On the asymptotics of the ratio of orthogonal polynomials.II, Mat. Sb. 118(160) (1982), 104-117.
11. E. A. Rakhmanov, English transl. in Math. USSR Sb. 46 (1983).
12. Gabor Szego, Orthogonal polynomials, 2nd ed., Amer. Math. Soc., Providence, R. I., 1959.
13. J. L.Walsh, Interpolation and approximation by rational functions in the complex domain, 2nd ed., Amer. Math. Soc., Providence, R. L, 1956.
14. G. Lopez Lagomasino and J. Ilian Gonzalez, Sobre la convergencia de los aproximantes multipuntuales de Pade para funciones de tipo Stieltjes, Cienc. Mat. (Havana) 2 (1981), 43-65.
15. Attila Mate, Paul Nevai, and Vilmos Totik, Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle, Constr. Approx. 1 (1985), 63-69.