Citation:
Advances in Computational Mathematics, 2007, vol. 26, n. 1-3, p. 81-104

ISSN:
1019-7168 (Print) 1572-9044 (Online)

DOI:
10.1007/s10444-004-7644-x

Sponsor:
The research was supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant number BFM2000-0015, as well as BFM2003-06335-C03-C02.

In the present paper we study the orthogonal polynomials with respect to a measure which is the sum of a finite positive Borel measure on [0,2π] and a Bernstein–Szegö measure. We prove that the measure sum belongs to the Szegö class and we obtain several propeIn the present paper we study the orthogonal polynomials with respect to a measure which is the sum of a finite positive Borel measure on [0,2π] and a Bernstein–Szegö measure. We prove that the measure sum belongs to the Szegö class and we obtain several properties about the norms of the orthogonal polynomials, as well as, about the coefficients of the expression which relates the new orthogonal polynomials with the Bernstein–Szegö polynomials. When the Bernstein–Szegö measure corresponds to a polynomial of degree one, we give a nice explicit algebraic expression for the new orthogonal polynomials.[+][-]

Description:

24 pages, no figures.-- MSC2000 codes: 33C47, 42C05.-- Dedicated to Professor Dr. Mariano Gasca with occasion of his 60th anniversary.