Szegö Transformations and Nth Order Associated Polynomials on the Unit Circle Articles uri icon

publication date

  • May 2009

start page

  • 1659

end page

  • 1671

issue

  • 10

volume

  • 57

international standard serial number (ISSN)

  • 0898-1221

electronic international standard serial number (EISSN)

  • 1873-7668

abstract

  • 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.