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

@article{Castillo2015ZerosOP, title={Zeros of para–orthogonal polynomials and linear spectral transformations on the unit circle}, author={Kenier Castillo and Francisco Marcell{\'a}n and Maria Das Neves Rebocho}, journal={Numerical Algorithms}, year={2015}, volume={71}, pages={699-714} }

We study the interlacing properties of zeros of para–orthogonal polynomials associated with a nontrivial probability measure supported on the unit circle dµ and para–orthogonal polynomials associated with a modification of dµ 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.

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The Kronecker polynomial K(z) is a finite product of cyclotomic polynomials Cj(z). Any Kronecker polynomial K(z) of degree N +1 with simple roots on the unit circle generates a finite set Φ0 =…

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C A ] 2 J ul 2 01 9 ZERO SPACING OF PARAORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE

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where Φ∗n(z) = z Φn(1/z). The sequence {αn}n=0 is often called the sequence of Verblunsky coefficients and Verblunsky’s Theorem asserts that there is a bijection between infinite sequences in D and…

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