On zeros of regular orthogonal polynomials on the unit circle
P. García Lázaro; F. Marcellán
Annales Polonici Mathematici (1993)
- Volume: 58, Issue: 3, page 287-298
- ISSN: 0066-2216
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topP. García Lázaro, and F. Marcellán. "On zeros of regular orthogonal polynomials on the unit circle." Annales Polonici Mathematici 58.3 (1993): 287-298. <http://eudml.org/doc/262299>.
@article{P1993,
abstract = {A new approach to the study of zeros of orthogonal polynomials with respect to an Hermitian and regular linear functional is presented. Some results concerning zeros of kernels are given.},
author = {P. García Lázaro, F. Marcellán},
journal = {Annales Polonici Mathematici},
keywords = {zeros; orthogonal polynomials; Toeplitz matrices; regular functional; Hermitian-Toeplitz matrix; moment functional; kernel polynomials},
language = {eng},
number = {3},
pages = {287-298},
title = {On zeros of regular orthogonal polynomials on the unit circle},
url = {http://eudml.org/doc/262299},
volume = {58},
year = {1993},
}
TY - JOUR
AU - P. García Lázaro
AU - F. Marcellán
TI - On zeros of regular orthogonal polynomials on the unit circle
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 3
SP - 287
EP - 298
AB - A new approach to the study of zeros of orthogonal polynomials with respect to an Hermitian and regular linear functional is presented. Some results concerning zeros of kernels are given.
LA - eng
KW - zeros; orthogonal polynomials; Toeplitz matrices; regular functional; Hermitian-Toeplitz matrix; moment functional; kernel polynomials
UR - http://eudml.org/doc/262299
ER -
References
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- [2] T. Erdelyi, P. Nevai, J. Zhang and J. S. Geronimo, Simple proof of Favard's theorem on the unit circle, Atti Sem. Mat. Fis. Univ. Modena 29 (1991), 41-46. Zbl0753.33004
- [3] G. Freud, Orthogonal Polynomials, Pergamon Press, Oxford, 1971.
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- [7] W. B. Jones, O. Njastad and W. J. Thron, Moment theory, orthogonal polynomials, quadrature, and continued fractions associated with the unit circle, Bull. London Math. Soc. 21 (1989), 113-152. Zbl0637.30035
- [8] M. G. Krein, On the distribution of the roots of polynomials which are orthogonal on the unit circle with respect to an alternating weight, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 2 (1966), 131-137.
- [9] H. J. Landau, Polynomials orthogonal in an indefinite metric, in: Orthogonal Matrix-Valued Polynomials and Applications, I. Gohberg (ed.), Birkhäuser, Basel, 1988, 203-214.
- [10] F. Marcellán, Orthogonal polynomials and Toeplitz matrices: Some applications, in: Rational Approximation and Orthogonal Polynomials, M. Alfaro (ed.), Publ. Sem. Mat. García de Galdeano, Zaragoza, 1989, 31-57.
- [11] F. Marcellán and M. Alfaro, Recent trends in orthogonal polynomials on the unit circle, in: Orthogonal Polynomials and their Applications, C. Brezinski et al. (eds.), IMACS Ann. Comput. Appl. Math. 9 (1991), 3-14.
- [12] G. Szegö, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ. 23, Providence, 1975.
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