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References

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A. Bultheel. Orthogonal matrix functions related to the multivariable Nevanlinna-Pick problem. Bull. Soc. Math. Belg. Sér. B, 32(2):149-170, 1980.
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A. Bultheel. On a special Laurent-Hermite interpolation problem. In L. Collatz, G. Meinardus, and H. Werner, editors, Numerische Methoden der Approximationstheorie 6, volume 59 of Internat. Ser. of Numer. Math., pages 63-79, Basel-New York-Berlin, 1981. Birkhäuser Verlag.
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A. Bultheel and P. Dewilde. Orthogonal functions related to the Nevanlinna-Pick problem. In P. Dewilde, editor, Proc. 4th Int. Conf. on Math. Theory of Networks and Systems at Delft, pages 207-212, North-Hollywood, 1979. Western Periodicals.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Orthogonal rational functions similar to Szego polynomials. In C. Brezinski, L. Gori, and A. Ronveaux, editors, Orthogonal Polynomials and their Applications, volume 9 of IMACS annals on computing and applied mathematics, pages 195-204, Basel, 1991. J.C. Baltzer AG.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. The computation of orthogonal rational functions and their interpolating properties. Numer. Algorithms, 2(1):85-114, 1992.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. A Favard theorem for orthogonal rational functions on the unit circle. Numer. Algorithms, 3:81-89, 1992.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. A moment problem associated to rational Szego functions. Numer. Algorithms, 3:91-104, 1992.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Orthogonal rational functions and quadrature on the unit circle. Numer. Algorithms, 3:105-116, 1992.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Moment problems and orthogonal functions. J. Comput. Appl. Math., 48:49-68, 1993.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Orthogonal rational functions on the unit circle and the real line. In P. Dewilde, M.A. Kaashoek, and M. Verhaegen, editors, Challenges of a Generalized System Theory, volume 40 of Essays of the Dutch Academy of Sciences, Sect. Physics, First series, pages 241-252, Amsterdam, 1993. North Holland.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Asymptotics for orthogonal rational functions. Trans. Amer. Math. Soc., 346:331-340, 1994.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Numerical quadratures on the unit circle: a survey with some new results. In M. Alfaro, A. Garcia, C. Jagels, and F. Marcellan, editors, Orthogonal Polynomials on the Unit Circle: Theory and Applications, pages 1-20, 1994.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. 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.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Quadrature formulas on the unit circle based on rational functions. J. Comput. Appl. Math., 50:159-170, 1994.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. 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.
16
A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Convergence of modified approximants associated with orthogonal rational functions. J. Comput. Appl. Math., 57(1/2):77-86, 1995.
17
A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Convergence of orthogonal rational functions. In R.M. Ali, St. Ruscheweyh, and E.B. Saff, editors, Computational Methods and Function Theory (CMFT'94), pages 111-123. World Scientific, 1995.
18
A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle. Numer. Algorithms, 13:321-344, 1996.
19
A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Orthogonal rational functions and modified approximants. Numer. Algorithms, 11:57-69, 1996.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Orthogonal rational functions and nested disks. J. Approx. Theory, 89:344-371, 1997.
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Orthogonal rational functions. Cambridge University Press, 1997. (To appear).
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A. Bultheel, P. González-Vera, E. Hendriksen, and O. Njåstad. Rates of convergence of multipoint rational approximants and quadrature formulas on the unit circle. J. Comput. Appl. Math., 77:77-102, 1997.
23
P. Dewilde and H. Dym. Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences. IEEE Trans. Inf. Th., IT-27:446-461, 1981.
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P. Dewilde and H. Dym. Lossless inverse scattering, digital filters, and estimation theory. IEEE Trans. Inf. Th., IT-30:644-662, 1984.
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M.M. Djrbashian. Expansions in systems of rational functions on a circle with a given set of poles. Doklady Akademii Nauk SSSR, 143:17-20, 1962. (In Russian. Translation in Soviet Mathematics Doklady, vol. 3, 315-319, 1962).
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M.M. Djrbashian. Orthogonal systems of rational functions on the unit circle with given set of poles. Doklady Akademii Nauk SSSR, 147:1278-1281, 1962. (In Russian. Translation in Soviet Mathematics Doklady, vol. 3, 1794-1798, 1962).
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M.M. Djrbashian. Orthogonal systems of rational functions on the circle. Izv. Akad. Nauk Armyan. SSR, 1:3-24, 1966. (In Russian).
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M.M. Djrbashian. Orthogonal systems of rational functions on the unit circle. Izv. Akad. Nauk Armyan. SSR, 1:106-125, 1966. (In Russian).
29
M.M. Djrbashian. Expansions by systems of rational functions with fixed poles. Izv. Akad. Nauk Armyan. SSR, 2:3-51, 1967. (In Russian).
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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. NATO-ASI, Kluwer Academic Publishers.
31
K. Müller and A. Bultheel. Translation of the Russian paper ``Orthogonal systems of rational functions on the unit circle'' by M.M.Djrbashian. Technical Report TW253, Department of Computer Science, K.U. Leuven, February 1997.



Karsten Mueller
Thu Oct 23 18:23:56 METDST 1997