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

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.