Zeros of para-orthogonal polynomials and linear spectral transformations on the unit circle Articles uri icon

publication date

  • March 2016

start page

  • 699

end page

  • 714

issue

  • 3

volume

  • 71

international standard serial number (ISSN)

  • 1017-1398

electronic international standard serial number (EISSN)

  • 1572-9265

abstract

  • We study the interlacing properties of zeros of para-orthogonal polynomials associated with a nontrivial probability measure supported on the unit circle d mu and para-orthogonal polynomials associated with a modification of d mu by the addition of a pure mass point, also called Uvarov transformation. Moreover, as a direct consequence of our approach, we present some results related with the Christoffel transformation.

keywords

  • para orthogonal polynomials; interlacing of zeros; uvarov transformation; christoffel transformation