Publication:
Orthogonal polynomials with respect to the sum of an arbitrary measure and a Bernstein-Szegö measure

Loading...
Thumbnail Image
Identifiers
ISSN: 1019-7168 (Print)
ISSN: 1572-9044 (Online)
Publication date
2007-01
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
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 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.
MR#: MR2350346 (2008m:33032)
Zbl#: Zbl 1109.33010
Keywords
Orthogonal polynomials, Bernstein–Szegö measure, Laguerre–Hahn affine functional
Bibliographic citation
Advances in Computational Mathematics, 2007, vol. 26, n. 1-3, p. 81-104