# 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

top- [1] R. L. Ellis, I. Gohberg and D. C. Lay, On two theorems of M. G. Krein concerning polynomials orthogonal on the unit circle, Integral Equations Operator Theory 11 (1988), 87-103. Zbl0639.46026
- [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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- [5] Y. L. Geronimus, Polynomials orthogonal on a circle and their applications, Amer. Math. Soc. Transl. Ser. 1, 3 (1962), 1-78.
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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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