Orthogonal Polynomials and Measures on The Unit Circle: The Geronimus Transformation Articles uri icon

publication date

  • January 2010

start page

  • 1220

end page

  • 1231

issue

  • 5

volume

  • 233

international standard serial number (ISSN)

  • 0377-0427

electronic international standard serial number (EISSN)

  • 1879-1778

abstract

  • In this paper we analyze a perturbation of a nontrivial positive measure supported on the unit circle. This perturbation is the inverse of the Christoffel transformation and is called the Geronimus transformation. We study the corresponding sequences of monic orthogonal polynomials as well as the connection between the associated Hessenberg matrices. Finally, we show an example of this kind of transformation. [Ejemplar dedicado a: William B. Gragg on the Occasion of His 70th Birthday]