On Some Classes of Polynomials Orthogonal on Arcs of the Unit Circle Connected with Symmetric Orthogonal Polynomials on an Interval

Journal of Approximation Theory

Volumn 94, Issue 1, 1998, Pages 73-106

  Zhedanov, Alexei ^a  

^a DONETSK NATIONAL UNIVERSITY   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003144795     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1998.3179     Document Type: Article

References (33)

1. Al-Salam W. A., Ismail M. E. H. A q-beta integral on the unit circle and some biorthogonal rational functions. Proc. Amer. Math. Soc. 121:1995;553-561.
2. Askey R. Comments. Gabor Szego: Collected Papers. 1982;Birkhäuser, Basel. p. 806-811.
3. Askey R., Wilson J. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Amer. Math. Soc. 54:1985;1-55.
4. Badkov V. M. Systems of orthogonal polynomials explicitly represented by the Jacobi polynomials. Math. Notes. 42:1987;858-863.
5. Bauer F. L. The g-algorithm. J. Soc. Indust. Appl. Math. 8:1960;1-17.
6. Cachafeiro A., Marcellan F. Modifications of Toeplitz matrices: Jump functions. Rocky Mountain J. Math. 23:1993;521-531.
7. Chihara T. S. An Introduction to Orthogonal Polynomials. 1978;Gordon & Breach, New York.
8. Delsarte P., Genin Y. The split Levinson algorithm. IEEE Trans. Acoust. Speech Signal Process. 34:1986;470-478.
9. Delsarte P., Genin Y. Tridiagonal approach to the algebraic environment of Toeplitz matrices I. Basic results. SIAM J. Matrix Anal. Appl. 12:1991;220-238.
10. Delsarte P., Genin Y. Tridiagonal approach to the algebraic environment of Toeplitz matrices. II. Zero and eigenvalue problems. SIAM J. Matrix Anal. Appl. 12:1991;432-448.
11. Gasper G., Rahman M. Basic Hypergeometric Series. 1990;Cambridge Univ. Press, Cambridge.
12. Geronimo J., Van Assche W. Orthogonal polynomials via polynomial mappings. Trans. Amer. Math. Soc. 308:1988;559-581.
13. Geronimus Ya. L. On the character of the solution of the moment in the case of limit-periodic associated fractions. Izv. Akad. Nauk SSSR Ser. Mat. 5:1941;203-210.
14. Geronimus Ya. L. Polynomials orthogonal on a circle and their applications. Amer. Math. Soc. Transl. Ser. 1. 1962;Amer. Math. Soc. Providence. p. 1-78.
15. Geronimus Ya. L. Orthogonal polynomials. Two Papers on Special Functions. Amer. Math. Soc. Transl. Ser. 2. 108:1977;Amer. Math. Soc. Providence. p. 37-130.
16. Golinskii L., Nevai P., Van Assche W. Perturbation of orthogonal polynomials on an arc of the unit circle. J. Approx. Theory. 83:1995;391-422.
17. Ismail M. E. H., Li Xin. On sieved orthogonal polynomials. IX. Orthogonality on the unit circle. Pacific J. Math. 153:1992;289-297.
18. Ismail M. E. H., Masson D. R. q-Hermite polynomials, biorthogonal rational functions and q-beta integrals. Trans. Amer. Math. Soc. 346:1994;63-116.
19. Ismail M. E. H., Rahman M. Ladder operators for Szego polynomials and related biorthogonal rational functions. Proc. Amer. Math. Soc. 124:1996;2149-2159.
20. Jones W. B., Thron W. J. Continued Fractions: Analytic Theory and Applications. Encyclopedia of Mathematics and Its Applications. 11:1980;Addison-Wesley, Reading.
21. Koekoek R., Swarttouw R. F. Report. 1994.
22. Karchev S., Mironov A. Integrable structures of unitary matrix models. Internat. J. Modern Phys. A. 7:1992;4803-4824.
23. Lasser R. Orthogonal polynomials and hupergroups. II. The symmetric case. Trans. Amer. Math. Soc. 341:1994;749-770.
24. Magnus A. Special nonuniform lattice (snul) orthogonal polynomials on discrete dense sets of points. J. Comput. Appl. Math. 65:1995;253-365.
25. Magnus A. Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials. J. Comput. Appl. Math. 57:1995;215-237.
26. Peherstorfer F., Steinbauer R. Orthogonal polynomials on arcs of the unit circle, I. J. Approx. Theory. 85:1996;140-184.
27. Ronveaux A. Discrete semi-classical orthogonal polynomials. J. Approx. Theory. 46:1986;403-407.
28. Spiridonov V., Vinet L., Zhedanov A. Difference Schrödinger operators with linear and exponential spectra. Lett. Math. Phys. 29:1993;63-73.
29. Spiridonov V., Zhedanov A. Discrete Darboux transformations, the discrete-time Toda lattice, and the Askey-Wilson polynomials. Methods Appl. Anal. 2:1996;369-398.
30. Szego G. Orthogonal Polynomials. 1975;Amer. Math. Soc. Providence.
31. Wall H. S. Some recent developments in the theory of continued fraction. Bull. Amer. Math. Soc. 47:1941;405-423.
32. Wall H. S. Analytic Theory of Continued Fractions. 1973;Chelsea, New York.
33. Widom H. The strong limit theorem for circular arcs. Indiana Univ. Math. J. 21:1971;277-283.