Zero distributions for discrete orthogonal polynomials

Journal of Computational and Applied Mathematics

Volumn 99, Issue 1-2, 1998, Pages 255-274

  Kuijlaars, A B J ^a   Rakhmanov, E A ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

Constrained equilibrium problem; Discrete orthogonality; Zero distribution

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; ESTIMATION; GREEN'S FUNCTION; LEAST SQUARES APPROXIMATIONS; PROBLEM SOLVING; THEOREM PROVING;

CONSTRAINED EQUILIBRIUM PROBLEM; DISCRETE ORTHOGONALITY; ORTHOGONAL POLYNOMIALS; ZERO DISTRIBUTION;

POLYNOMIALS;

EID: 0032207940     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00161-7     Document Type: Article

References (38)

1. V.S. Buyarov, Logarithmic asymptotics of polynomials that are orthogonal on ℝ with nonsymmetric weight, Mat. Zametki 50 (1991) 28-36, English transl. in Math. Notes 50 (1991) 789-795.
2. V.S. Buyarov, Logarithmic asymptotics of polynomials that are orthogonal on ℝ with nonsymmetric weight, Mat. Zametki 50 (1991) 28-36, English transl. in Math. Notes 50 (1991) 789-795.
3. V.S. Buyarov, E.A. Rakhmanov, On the families of equilibrium measures in an external field on the real line, manuscript.
4. P.L. Chebyshev, Interpolation of equidistant nodes, and, on continued fractions, in: Complete Works, USSR Academy of Sciences Publishing House, Moscow-Leningrad, 1948; French transl., Oeuvres, Chelsea, New York, 1962.
5. P.L. Chebyshev, Interpolation of equidistant nodes, and, on continued fractions, in: Complete Works, USSR Academy of Sciences Publishing House, Moscow-Leningrad, 1948; French transl., Oeuvres, Chelsea, New York, 1962.
6. L-C. Chen, M.E.H. Ismail, Asymptotics of Racah coefficients and polynomials, manuscript.
7. T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
8. D. Coppersmith, T.J. Rivlin, The growth of polynomials bounded at equally spaced points, SIAM J. Math. Anal. 23 (1992) 970-983.
9. P. Deift, K.T-R. McLaughlin, A continuum limit of the Toda lattice, Mem. Amer. Math. Soc. 131 (1998).
10. S.B. Damelin, E.B. Saff, Asymptotics of weighted polynomials on varying sets, manuscript.
11. P.D. Dragnev, E.B. Saff, Constrained energy problems with applications to orthogonal polynomials of a discrete variable, J. Anal. Math. 72 (1997) 223-259.
12. P.D. Dragnev, E.B. Saff, A problem in potential theory and zero asymptotics of Krawtchouk polynomials, manuscript.
13. A.A. Gonchar, E.A. Rakhmanov, Equilibrium measure and distribution of the zeros of extremal polynomials, Mat. Sb. 125 (1984) 117-127; English transl. in Math. USSR-Sb. 53 (1986) 119-130.
14. A.A. Gonchar, E.A. Rakhmanov, Equilibrium measure and distribution of the zeros of extremal polynomials, Mat. Sb. 125 (1984) 117-127; English transl. in Math. USSR-Sb. 53 (1986) 119-130.
15. M.E.H. Ismail, P. Simeonov, Strong asymptotics for Krawchuk polynomials, manuscript.
16. X.S. Jin, R. Wong, Uniform asymptotic expansions for Meixner polynomials, manuscript.
17. A.B.J. Kuijlaars, W. Van Assche, Extremal polynomials on discrete sets, manuscript.
18. A.B.J. Kuijlaars, W. Van Assche, The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients, manuscript.
19. V.I. Levenshtein, Krawtchouk polynomials and universal bounds for codes and design in Hamming spaces, IEEE Trans. Inform. Theory 41 (1995) 1303-1321.
20. G. Lopez, E.A. Rakhmanov, Rational approximations, orthogonal polynomials and equilibrium distributions, in: Alfaro et al. (Eds.), Orthogonal Polynomials and their Applications Lecture Notes in Math., vol. 1329, Springer, Berlin, 1988, pp. 125-156.
21. D.S. Lubinsky, An update on orthogonal polynomials and weighted approximation on the real line, Acta Appl. Math. 33 (1993) 121-164.
22. H.N. Mhaskar, E.B. Saff, Extremal problems for polynomials with exponential weights, Trans. Amer. Math. Soc. 285 (1984) 203-234.
23. A.F. Nikiforov, S.K. Suslov, V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991.
24. G. Ponzano, T. Regge, Semiclassical limit of Racah coefficients, in: Spectroscopic and Group Theoretical Methods in Physics, North-Holland, Amsterdam, 1969, pp. 1-58.
25. E.A. Rakhmanov, On asymptotic properties of polynomials orthogonal on the real axis, Mat. Sb. 119 (1982) 163-203; English transl. in Math. USSR-Sb. 47 (1984) 155-193.
26. E.A. Rakhmanov, On asymptotic properties of polynomials orthogonal on the real axis, Mat. Sb. 119 (1982) 163-203; English transl. in Math. USSR-Sb. 47 (1984) 155-193.
27. E.A. Rakhmanov, Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable, Mat. Sb. 187 (1996) 109-124; English transl. in Sb. Math. 187 (1996) 1213-1228.
28. E.A. Rakhmanov, Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable, Mat. Sb. 187 (1996) 109-124; English transl. in Sb. Math. 187 (1996) 1213-1228.
29. E.A. Rakhmanov, On bounds for polynomials with unit discrete norms, manuscript.
30. B. Rui, R. Wong, Uniform asymptotic expansion of Charlier polynomials, Meth. Appl. Anal. 1 (1994) 294-313.
31. E.B. Saff, V. Totik, Logarithmic Potentials with External Fields, Springer, New York, 1997.
32. I.I. Sharapudinov, Asymptotic properties of Krawtchouk polynomials, Mat. Zametki 44 (1988) 682-693; English transl. in Math. Notes 44 (1988) 855-862.
33. I.I. Sharapudinov, Asymptotic properties of Krawtchouk polynomials, Mat. Zametki 44 (1988) 682-693; English transl. in Math. Notes 44 (1988) 855-862.
34. I.I. Sharapudinov, Asymptotic properties of the Hahn orthogonal polynomials of a discrete variable, Mat. Sb. 180 (1989) 1259-1277; English transl. in Math. USSR-Sb. 68 (1991).
35. I.I. Sharapudinov, Asymptotic properties of the Hahn orthogonal polynomials of a discrete variable, Mat. Sb. 180 (1989) 1259-1277; English transl. in Math. USSR-Sb. 68 (1991).
36. H. Stahl, V. Totik, General Orthogonal Polynomials, Cambridge University Press, Cambridge, 1992.
37. G. Szego, Orthogonal Polynomials, AMS Colloquium Publications 23, 4th ed., Amer. Math. Soc., Providence, RI, 1975.
38. W. Van Assche, Asymptotics for Orthogonal Polynomials, Lecture Notes in Math., vol. 1265, Springer, Berlin, 1987.