On the “Favard theorem” and its extensions

In this paper we present a survey on the “Favard theorem” and its extensions. c 2001 Elsevier Science B.V. All rights reserved.

[1]  On polynomials with interlacing zeros , 1985 .

[2]  M. Alfaro,et al.  On zeros of polynomials orthogonal with respect to a quasi-definite inner product on the unit circle , 1995 .

[3]  Francisco Marcellán,et al.  On recurrence relations for Sobolev orthogonal polynomials , 1995 .

[4]  Claude Brezinski,et al.  Polynômes orthogonaux et applications , 1985 .

[5]  L. Lichtenstein,et al.  Spektraltheorie der unendlichen Matrizen : Einführung in den analytischen Apparat der Quantenmechanik , 1929 .

[6]  S. Barnett.  Polynomials and linear control systems , 1983 .

[7]  J. Shohat,et al.  The Relation of the Classical Orthogonal Polynomials to the Polynomials of Appell , 1936 .

[8]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

[9]  Francisco Marcellán Español,et al.  A Class of Matrix Orthogonal Polynomials on the Unit Circle , 1989 .

[10]  A. Atzmon.  n-Orthonormal Operator Polynomials , 1988 .

[11]  J. Rassias.  Solution of a problem of Ulam , 1989 .

[12]  Orthogonal Matrix-valued Polynomials and Applications , 1988 .

[13]  M. P. Alfaro,et al.  Solution of a problem of P. Tura´n on zeros of orthogonal polynomials on the unit circle , 1988 .

[14]  Helly.  Spektraltheorie der unendlichen Matrizen , 1930 .

[15]  On the numerators of the convergents of the Stieltjes continued fractions , 1933 .

[16]  Zeros extrêmaux de polynômes orthogonaux , 1985 .

[17]  I. P. Natanson.  Constructive function theory , 1964 .

[18]  Francisco Marcellán,et al.  On a Class of Matrix Orthogonal Polynomials on the Real Line , 1993 .

[19]  T. Chihara,et al.  An Introduction to Orthogonal Polynomials , 1979 .

[20]  I︠a︡. L. Geronimus.  Polynomials orthogonal on a circle and their applications , 1954 .

[21]  Walter Van Assche,et al.  Orthogonal matrix polynomials and higher-order recurrence relations , 1993 .

[22]  H. Landau.  Maximum entropy and the moment problem , 1987 .

[23]  T. Stieltjes.  Recherches sur les fractions continues , 1995 .

[24]  Burton Wendroff.  On orthogonal polynomials , 1961 .

[25]  A. J. Durán.  A Generalization of Favard's Theorem for Polynomials Satisfying a Recurrence Relation , 1993 .