Spectral transformations for Hermitian Toeplitz matrices

In this paper we deal with some perturbations of probability measures supported on the unit circle as well as, in a more general framework, with Hermitian linear functionals. We focus our attention in the Hessenberg matrix associated with the multiplication operator in terms of an orthogonal basis in the linear space of polynomials with complex coefficients. The LU and QR factorizations of such a matrix are introduced. Then, the connection between the above-mentioned perturbations and such factorizations is presented.