A Cubic decomposition of sequences of orthogonal polynomials on the unit circle

15 pages, no figures.-- MSC2000 codes: 42C05.MR#: MR1925172 (2003g:42039)Zbl#: Zbl 1026.42026In this paper we will discuss the problem of generation of sequences of orthogonal polynomials with respect to measures supported on the unit circle from a given sequence of orthogonal polynomials using a perturbation of a cubic sieved process. The basic tools are the Szegö forward recurrence relation as well as the fact of the coprimality of orthogonal polynomials on the unit circle and their corresponding reverse polynomials. We also give the connection between the associated orthogonality measures. Finally, some examples of this cubic decomposition are shown.The work of the first author was supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant BFM 2000-0206-C04-03. The work of the second author was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB 98-1615. The work of the third author was supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant BFM 2000-0206-C04-01 and INTAS project 2000-272.Publicad