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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-ortogonal polynomials that follows from these Szeg˝ o polynomials are also considered. With two particular choice of real values (positive and… (More)

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