On rational transformations of linear functionals: direct problem

13 pages, no figures.-- MSC2000 codes: 33C47, 42C05.MR#: MR2086540 (2005f:42051)Zbl#: Zbl 1066.33008Let u be a quasi-definite linear functional. We find necessary and sufficient conditions in order to the linear functional v satisfying $(x-\tilde{a})u=\lambda(x-a)v$ be a quasi-definite one. Also we analyze some linear relations linking the polynomials orthogonal with respect to u and v.M.A. and M.L.R. were partially supported by MCYT Grant BFM 2003-06335-C03-03 (Spain), FEDER funds (EU), and DGA E-12/25 (Spain). F.M. was partially supported by MCYT Grant BFM 2003-06335-C03-02 (Spain) and INTAS Research Network NeCCA INTAS 03-51-66378. A.P. was partially supported by MCYT Grant BFM 2001-1793 (Spain), FEDER funds (EU), and DGA E-12/25 (Spain).Publicad