Asymptotic Behaviour of Orthogonal Polynomials on the Unit Circle with Asymptotically Periodic Reflection Coefficients: II. Weak Asymptotics

Journal of Approximation Theory

Volumn 105, Issue 1, 2000, Pages 102-128

  Peherstorfer, Franz ^a   Steinbauer, Robert ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Orthogonal polynomials; unit circle; arcs; weak asymptotics; asymptotically periodic reflection coefficients; reproducing kernel function

Indexed keywords

EID: 0005867940     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.2000.3450     Document Type: Article

References (23)

1. Barrios Rolania D., López G. Ratio asymptotics for polynomials orthogonal on arcs of the unit circle. Constr. Approx. 15:1999;1-31.
2. p Spaces. Pure and Applied Mathematics. 38:1970;Academic Press, New York/London.
3. Geronimus Ya. L. On the character of the solutions of the moment problem in the case of a limit-periodic associated fraction. Izv. Akad. Nauk SSSR Ser. Mat. 5:1941;203-210.
4. Geronimus Ya. L. On polynomials orthogonal on the circle, on the trigonometric moment-problem and on allied Caratheodory and Schur Functions. C.R. (Doklady) Acad. Sci. URSS (N.S.). 29:1943;291-295.
5. Geronimus Ya. L. On polynomials orthogonal on a circle, on the trigonometric moment problem, and on the associated functions of Caratheodory's and Schur's type. Mat. Sb. (N.S.). 15:1944;99-130.
6. Geronimus Ya. L. Polynomials orthogonal on a circle and their applications. Amer. Math. Soc. Transl. 1962;Amer. Math. Soc. Providence. p. 1-78.
7. Geronimus Ya. L. Orthogonal Polynomials. 1961;Consultants Bureau, New York.
8. Golinskii L., Nevai P., Van Assche W. Perturbation of orthogonal polynomials on an arc of the unit circle. J. Approx. Theory. 83:1995;392-422.
9. Levinson N. Simplified treatment of integrals of Cauchy type, the Hilbert problem and singular integral equations; Appendix: Poincaré-Bertrand formula. SIAM Rev. 7:1965;474-502.
10. Máté A., Nevai P., Totik V. Extension of Szego's theory of orthogonal polynomials, II. Constr. Approx. 3:1987;51-72.
11. Muschelischwili N. I. Singuläre Integralgleichungen. 1965;Akademie-Verlag, Berlin.
12. Peherstorfer F. Gauss-Tchebycheff quadrature formulas. Numer. Math. 58:1990;273-286.
13. Peherstorfer F. A special class of polynomials orthogonal on the unit circle including associated polynomials. Constr. Approx. 12:1996;161-186.
14. Peherstorfer F., Steinbauer R. Orthogonal polynomials on arcs of the unit circle, I. J. Approx. Theory. 85:1996;140-184.
15. Peherstorfer F., Steinbauer R. Orthogonal polynomials on arcs of the unit circle. II. Orthogonal polynomials with periodic reflection coefficients. J. Approx. Theory. 87:1996;60-102.
16. Peherstorfer F., Steinbauer R. Asymptotic behaviour of orthogonal polynomials on the unit circle with asymptotically periodic reflection coefficients. J. Approx. Theory. 88:1997;316-353.
17. F. Peherstorfer, and, R. Steinbauer, Strong asymptotics of orthonormal polynomials with the aid of Green's function, SIAM J. Math. Anal, in press.
18. Rahmanov E. A. On the asymptotics of the ratio of orthogonal polynomials. Math. USSR Sb. 32:1977;199-213.
19. Rahmanov E. A. On the asymptotics of the ratio of orthogonal polynomials, II. Math. USSR Sb. 46:1983;105-117.
20. Szego G. Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ. 23:1975;Amer. Math. Soc. Providence.
21. Turán P. On orthogonal polynomials. Anal. Math. 1:1975;297-311.
22. Van Assche W. Christoffel functions and Turán determinants on several intervals. J. Comput. Appl. Math. 48:1993;207-223.
23. Widom H. Extremal polynomials associated with a spectrum of curves in the complex plane. Adv. Math. 3:1969;127-232.