Kenier Castillo

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The objective of this manuscript is to study directly the Favard type theorem associated with the three term recurrence formula Rn+1(z) =  (1 + icn+1)z + (1 − icn+1)  Rn(z) − 4dn+1z Rn−1(z), n ≥ 1, with R0(z) = 1 and R1(z) = (1 + ic1)z + (1 − ic1), where {cn} ∞ n=1 is a real sequence and {dn} ∞ n=1 is a positive chain sequence. We establish that there(More)
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 FL. We show that a rational spectral transformation of FL with polynomial coefficients is a finite composition of four canonical spectral transformations.
In this contribution, we study the sequences of orthogonal polynomials with respect to the Sobolev inner product $$ \langle{f,g}\rangle_{S}:=\int_{\mathbb{T}} f(z) \overline{g(z)} d\mu(z) + \lambda f^{(j\,)}(\alpha)\overline{g^{(j\,)}(\alpha)}, $$ where μ is a nontrivial probability measure supported on the unit circle, α ∈ ℂ, $\lambda \in(More)
We study polynomials which satisfy the same recurrence relation as the Szegő 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 Szegő polynomials are also considered. With positive values for the reflection coefficients, zeros of(More)