Zeros of polynomials orthogonal on two arcs of the unit circle

Journal of Approximation Theory

Volumn 132, Issue 1, 2005, Pages 42-71

  Lukashov, A L ^a,b   Peherstorfer, Franz ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b SARATOV STATE UNIVERSITY   (Russian Federation)

Author keywords

Orthogonal polynomials; Two arcs; Zeros

Indexed keywords

EID: 11444251855     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jat.2004.10.009     Document Type: Article

References (33)

1. N.I. Achieser, Elements of the theory of elliptic functions, Translations of Mathematical Monographs, vol. 79, American Mathematical Society, Providence, RI, 1990
2. A.I. Aptekarev Asymptotic properties of polynomials orthogonal on a system of contours and periodic motions of Toda lattices, Math. USSR Sb. 53 1986 233-260
3. V.I. Buslaev The Baker-Gammel-Wills conjecture in the theory of Padé approximants Russian Math. Sb. 194 2003 43-66
4. L. Fejér Über die Lage der Nullstellen von Polynomen, die aus Minimum forderungen gewisser Art entspringen Math. Ann. 85 1922 41-48
5. B. Fischer Polynomial Based Iteration Methods for Symmetric Linear Systems 1996 Wiley-Teubner Chicester
6. J.S. Geronimo R. Johnson An inverse problem associated with polynomials orthogonal on the unit circle Comm. Math. Phys. 193 1998 125-150
7. Ya.L. Geronimus Polynomials orthogonal on a circle and their applications Amer. Math. Soc. Transl. 3 1962 1-78
8. S.V. Khrushchev Classification theorems for general orthogonal polynomials on the unit circle J. Approx. Theory 116 2002 268-342
9. È.I. Krupickǐ On a class of polynomials deviating least from zero on two intervals Sov. Math. Dokl. 2 1961 657-660
10. D.S. Lubinsky Rogers-Ramanujan and the Baker-Gammel-Wills (Padé) conjecture Ann. Math. (2) 157 2003 847-889
11. A.L. Lukashov, Reflection coefficients for orthogonal polynomials on several arcs of the unit circle, Matem. Sbornik 195(11) (2004) 95-118 (in Russian)
12. A.L. Lukashov Inequalities for derivatives of rational functions on several intervals Izv. Math. 68 2004 543-565
13. A.L. Lukashov, F. Peherstorfer, Asymptotic behaviour of zeros of orthogonal polynomials on arcs of the unit circle, in work
14. F. Peherstorfer Orthogonal and extremal polynomials on several intervals J. Comput. Appl. Math. 48 1993 187-205
15. F. Peherstorfer Elliptic orthogonal and extremal polynomials Proc. London. Math. Soc. 70 1995 605-624
16. F. Peherstorfer On the zeros of orthogonal polynomials elliptic case Constr. Approx. 20 2004 377-397
17. F. Peherstorfer Zeros of polynomials orthogonal on several intervals Internat. Math. Res. Notices 7 2003 361-385
18. F. Peherstorfer R. Steinbauer Characterization of orthogonal polynomials with respect to a functional J. Comput. Appl. Math. 65 1995 339-355
19. F. Peherstorfer R. Steinbauer Orthogonal polynomials on arcs of the unit circle, I J. Approx. Theory 85 1996 140-184
20. F. Peherstorfer R. Steinbauer Orthogonal polynomials on arcs of the unit circle, II. Orthogonal polynomials with periodic reflection coefficients J. Approx. Theory 87 1996 60-102
21. F. Peherstorfer R. Steinbauer Asymptotic behaviour of orthogonal polynomials on the unit circle with asymptotically periodic reflection coefficients J. Approx. Theory 88 1997 316-353
22. F. Peherstorfer R. Steinbauer Strong asymptotics of orthonormal polynomials with the aid of Green's function SIAM J. Math. Anal. 32 2000 385-402
23. F. Peherstorfer R. Steinbauer Orthogonal polynomials on the circumference and arcs of the circumference J. Approx. Theory 102 2000 96-119
24. A.P. Petukhov On snakes and approximation of discontinuous functions in the Hausdorff metric Anal. Math. 11 1985 55-73
25. B. Simon, Orthogonal polynomials in the circle, I: The basics, preprint
26. E.B. Saff Orthogonal polynomials from a complex perspective in: P. Nevai (Ed.) Orthogonal Polynomials Theory and Practice 1990 Kluwer Academic Publishers Dordrecht 363-393
27. H. Stahl V. Totik General Orthogonal Polynomials 1992 Cambridge University Press Cambridge
28. S.P. Suetin Padé approximants and efficient analytic continuation of a power series Russian Math. Surveys 57 2002 43-141
29. G. Szego On a problem of the best approximation Abh. Math. Sem. Univ. Hamburg 27 1964 193-198
30. J. Tannery J. Molk Elements de la théorie des fonctions elliptiques, tom. I 1972 Chelsea New York
31. Yu.Ya. Tomchuk Orthogonal polynomials on a given system of arcs of the unit circle Sov. Math. Dokl. 4 1963 931-934
32. H. Widom Polynomials associated with measures in the complex plane J. Math. Mech. 16 1967 997-1013
33. H. Widom Extremal polynomials associated with a system of curves in the complex plane Adv. Math. 3 1969 127-232