Convergence of orthogonal rational functions outside of the unit circle

Journal of Computational and Applied Mathematics

Volumn 69, Issue 2, 1996, Pages 345-351

  Pan, K ^a  

^a BARRY UNIVERSITY   (United States)

Author keywords

Orthogonal rational functions

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; POLES AND ZEROS; POLYNOMIALS; SET THEORY;

BOREL MEASURE; FINITE BLASCHKE PRODUCT; HILBERT SPACE; ORTHOGONAL RATIONAL FUNCTIONS; UNIT CIRCLE;

COMPUTATIONAL METHODS;

EID: 0030142809     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(95)00046-1     Document Type: Article

References (18)

1. A. Bultheel, P. González-Vera, E. Hendriksen and O. Njåstad, A Szego theory for rational functions, Tech. Report TW-131, Dept. of Computer Science, K.U. Leuven, May 1990.
2. A. Bultheel, P. González-Vera, E. Hendriksen and O. Njåstad, The computation of orthogonal rational functions and their interpolating properties, Numer. Algorithms 2 (1992) 85-114.
3. A. Bultheel, P. González-Vera, E. Hendriksen and O. Njåstad, A Favard theorem for orthogonal rational functions on the unit circle, Numer. Algorithms 3 (1992) 81-89.
4. A. Bultheel, P. González-Vera, E. Hendriksen and O. Njåstad, Moment problems and orthogonal functions, J. Comput. Appl. Math. 48 (1-2) (1993) 49-68.
5. A. Bultheel, P. González-Vera, E. Hendriksen and O. Njåstad, Recurrence relations for orthogonal functions, in: S.C. Cooper and W.J. Thron, Eds., Continued Fractions and Orthogonal Functions (Marcel Dekker, New York, 1994) 23-46.
6. A. Bultheel, P. González-Vera, E. Hendriksen and O. Njåstad, Asymptotics for orthogonal rational functions, preprint, 1993.
7. A. Bultheel, P. González-Vera, E. Hendriksen and O. Njåstad, Convergence of orthogonal rational functions, preprint, 1994.
8. P. Delsarte and Y. Genin, On the role of orthogonal polynomials on the unit circle in digital signal processing applications, in: P. Nevai, Ed., Orthogonal Polynomials: Theory and Practice (Kluwer, Dordrecht, 1990) 115-113.
9. P. Dewilde and H. Dym, Schur recursion, error formulas, and convergence of rational estimators for stationary stochastic sequences, IEEE Trans. Inform. Theory IT27 (1981) 446-461.
10. M.M. Djrbashian, Orthonormal sets of rational functions on the unit circle with given set of poles, Doklady SSSR 147 (1962) 1278-1281 (in Russian).
11. M.M. Djrbashian, Orthogonal systems of rational functions on the circle, Izv. Akad. Nauk Armjan. SSR. Ser. Mat. 1(1) (1966) 3-24 (in Russian).
12. M.M. Djrbashian, Orthogonal systems of rational functions on the unit circle, Izv. Akad. Nauk Armjan. SSR. Ser. Mat. 1(2) (1966) 106-125 (in Russian).
13. M.M. Djrbashian, A survey on the theory of orthogonal systems and some open problems, in: P. Nevai, Ed., Orthogonal Polynomials: Theory and Practice (Kluwer, Dordrecht, 1990) 135-146.
14. X. Li and K. Pan, Strong and weak convergence of rational functions orthogonal on the circle, J. London Math. Soc., to appear.
15. K. Pan, Strong and weak convergence of orthogonal systems of rational functions on the unit circle, J. Comput. Appl. Math. 46 (1993) 427-436.
16. K. Pan, Extensions of Szegö's theory of rational functions orthogonal on the unit circle, J. Comput. Appl. Math. 62(3) (1995) 321-331.
17. K. Pan, Convergence of rational functions orthogonal on the unit circle, submitted.
18. J.L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, Amer. Math. Soc. Colloq. Publ. 20 (Amer. Math. Soc., Providence, RI, 5th ed., 1969).