We develop a theory of Darboux transformations for CMV matrices, canonical
representations of the unitary operators. In perfect analogy with their self-adjoint version–the …

The aim of this paper is to analyze the relation between the Christoffel transformations in the
framework of hermitian linear functionals and the associated polynomials of the second kind …

In this paper we consider transformations of sequences of orthogonal polynomials
associated with a Hermitian linear functional $\mathcal {L} $ using spectral transformations …

This paper is devoted to the study of direct and inverse (Laurent) polynomial modifications of
moment functionals on the unit circle, ie, associated with hermitian Toeplitz matrices. We …

We consider the sequences of matrix bi-orthogonal polynomials with respect to the bilinear
forms\left ⟨ ⋅, ⋅\right ⟩ _ ̂ R·,· R^ and\left ⟨ ⋅, ⋅\right ⟩ _ ̂ L·,· L^ ⟨ P (z_1), Q (z_2) ⟩ _ ̂ …

The main purpose of the work presented here is to study transforma-tions of sequences of
orthogonal polynomials associated with a hermitian linear functional L, using spectral …

This paper is devoted to the study of general (Laurent) polynomial modifications of moment
functionals on the unit circle, ie, associated with hermitian Toeplitz matrices. We present a …

The main purpose of the work presented here is to study transformations of sequences of
orthogonal polynomials associated with a hermitian linear functional L, using spectral …

In this paper we present some recent results concerning linear spectral transformations of
Carath\'eodory functions. More precisely, given two Carath\'eodory functions related by a …

In this paper we obtain a difference equation relating the Schur parameters of two quasi-
definite hermitian linear functionals connected by an arbitrary rational modification …