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

Publication . Rebocho, Maria das Neves; Castillo, Kenier; Marcellan, Francisco

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.

2016Journal article

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Characterization theorem for Laguerre- Hahn orthogonal polynomials on non-uniform lattices

Publication . Rebocho, M. N.; Branquinho, A.

A characterization theorem for Laguerre–Hahn orthogonal polynomials on non-uniform lattices is stated and proved.This theorem proves the equivalence between the Riccati equation for the formal Stieltjes function, linear first-order difference relations for the orthogonal polynomials as well as for the associated polynomials of the first kind, and linear first-order difference relations for the functions of the second kind.

2015Journal article

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