Orthogonal rational functions and interpolatory product rules on the unit circle. i. recurrence and interpolation

Analysis (Germany)

Volumn 18, Issue 2, 1998, Pages 167-184

  Bultheel, A ^a   Gonzalez Vera, P ^a   Hendriksen, E ^a   Njastad O ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012999386     PISSN: 01744747     EISSN: 21966753     Source Type: Journal    
DOI: 10.1524/anly.1998.18.2.167     Document Type: Article

References (17)

1. A. Bultheel. Laurent series and their PadeA approximations, volume 27 of Oper. Theory: Adv. Appl. BirkhaUuser Verlag, Basel-Boston, 1987.
2. A. Bultheel and P. Dewilde. Orthogonal functions related to the Nevanlinna-Pick problem. In P. Dewilde, editor, Proc. J,th Int. Conf. on Math. Theory of Networks and Systems at Delft, pages 207–212, North-Hollywood, 1979. Western Periodicals.
3. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. The computation of orthogonal rational functions and their interpolating properties. Numer. Algorithms, 2(1):85–114, 1992.
4. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. Moment problems and orthogonal functions. J. Comput. Appl. Math., 48:49–68, 1993.
5. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. Orthogonal rational functions on the unit circle: theory, applications and generalizations. In M. Alfaro, A. Garcia, C. Jagels, and F. Marcellan, editors, Orthogonal Polynomials on the Unit Circle: Theory and Applications, pages 21–42, 1994.
6. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. Quadrature formulas on the unit circle based on rational functions. J. Comput. Appl. Math., 50:159–170, 1994.
7. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. NjaUstad. Recurrence relations for orthogonal functions. In S.C. Cooper and W.J. Thron, editors, Continued Fractions and Orthogonal Functions, volume 154 of Lecture Notes in Pure and Appl. Math., pages 24–46. Marcel Dekker, 1994.
8. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. NjaCstad. Orthogonal rationell functions and nested disks. J. Approx. Theory, 89:344–371, 1997.
9. M.M. Djrbashian. A survey on the theory of orthogonal systems and some open problems. In P. Nevai, editor, Orthogonal polynomials: Theory and practice, volume 294 of Series C: Mathematical and Physical Sciences, pages 135–146, Boston, 1990. NATOASI, Kluwer Academic Publishers.
10. W.B. Jones and W.J. Thron. Continued Fractions. Analytic Theory and Applications. Addison-Wesley, Reading, Mass., 1980.
11. X. Li and K. Pan. Strong and weak convergence of rational functions orthogonal on the unit circle. J. London Math. Soc., 53:289–301, 1996.
12. G.L. Lopez [LoApez-Lagomasino]. Szego's theorem for orthogonal polynomials with respect to varying measures. In M. Alfaro et al., editors, Orthogonal polynomials and their applications, volume 1329 of Lecture Notes in Math., pages 255–260. Springer, 1988.
13. G.L. Lopez [LoApez-Lagomasino]. Asymptotics of polynomials orthogonal with respect to varying measures. Constr. Approx., 5:199–219, 1989.
14. L. Lorentzen and H. Waadeland. Continued fractions vnth applications, volume 3 Studies in Computational Mathematics. North-Holland, 1992.
15. K. Pan. On orthogonal systems of rational functions on the unit circle and polynomials orthogonal with respect to varying measures. J. Comput. Appl. Math., 47(3):313–322, 1993.
16. K. Pan. Extensions of Szego's theory of rational functions orthogonal on the unit circle. J. Comput. Appl. Math., 62:321–331, 1995.
17. W.J. Thron. L-polynomials orthogonal on the unit circle. In. A.M. Cuyt, editor, Nonlinear Numerical Methods and Rational Approximation, pages 271–278. Kluwer, 1988.