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1993 | 58 | 3 | 287-298
Tytuł artykułu

On zeros of regular orthogonal polynomials on the unit circle

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
58
Numer
3
Strony
287-298
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-08-28
poprawiono
1993-06-14
Twórcy
  • Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Politécnica, C/José Gutierrez Abascal, 2, 28006 Madrid, Spain
  • Departamento de Ingenieria, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida Mediterraneo 20, 28913 Leganes (Madrid), Spain
Bibliografia
  • [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.
  • [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.
  • [3] G. Freud, Orthogonal Polynomials, Pergamon Press, Oxford, 1971.
  • [4] P. Garcí a Lázaro, Polinomios ortogonales y distribuciones, Doctoral Dissertation, Publ. Sem. Mat. García de Galdeano, Ser. II, 32, Universidad de Zaragoza, 1990.
  • [5] Y. L. Geronimus, Polynomials orthogonal on a circle and their applications, Amer. Math. Soc. Transl. Ser. 1, 3 (1962), 1-78.
  • [6] E. Godoy and F. Marcellán, Orthogonal polynomials on the unit circle: Distribution of zeros, J. Comput. Appl. Math. 37 (1991), 265-272.
  • [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.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv58z3p287bwm
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