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- Zeros of para-orthogonal polynomials and linear spectral transformations on the unit circlePublication . Rebocho, Maria das Neves; Castillo, Kenier; Marcellan, FranciscoWe 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.
- On linear spectral transformations and the Laguerre-Hahn classPublication . Rebocho, M. N.; Castillo, KenierWe study the Christoffel, Geronimus, and Uvarov transformations for Laguerre-Hahn orthogonal polynomials on the real line. It is analysed the modification of the corresponding difference-differential equations that characterize the systems of orthogonal polynomials and the consequences for the three-term recurrence relation coefficients.