Garza, LuisMarcellán Español, Francisco José2009-12-022009-12-022009-05Computers and Mathematics with Applications, 2009, vol. 57, n. 10, p. 1659-16710898-1221https://hdl.handle.net/10016/590113 pages, no figures.-- MSC2000 codes: 42C05, 15A23.In this paper we analyze the Stieltjes functions defined by the Szegö inverse transformation of a nontrivial probability measure supported on the unit circle such that the corresponding sequence of orthogonal polynomials is defined by either backward or forward shifts in their Verblunsky parameters. Such polynomials are called anti-associated (respectively associated) orthogonal polynomials. Thus, rational spectral transformations appear in a natural way.application/pdfeng© ElsevierProbability measuresSzegö transformationsOrthogonal polynomialsNth associated orthogonal polynomialsVerblunsky parametersRational spectral transformationsCarathéodory and Stieltjes functionsresearch articleMatemáticas10.1016/j.camwa.2009.03.040restricted access