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In this paper we consider transformations of sequences of orthogonal polynomials associated with a Hermitian linear functional L using spectral transformations of the corresponding C-function F L. We show that a rational spectral transformation of F L with polynomial coefficients is a finite composition of four canonical spectral transformations.
We study polynomials which satisfy the same recurrence relation as the Szeg˝ o polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szeg˝ o polynomials are also considered. With positive values for the reflection coefficients, zeros… (More)
We study the interlacing properties of zeros of para–orthogonal polynomials associated with a nontrivial probability measure supported on the unit circle d µ and para–orthogonal polynomials associated with a modification of d µ by the addition of a pure mass point, also called Uvarov transformation. Moreover, as a direct consequence of our approach, we… (More)