On the semiclassical character of orthogonal polynomials satisfying structure relations

We prove the semiclassical character of some sequences of orthogonal polynomials [...]info:eu-repo/semantics/publishedVersio

Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle

In this paperwe characterize sequences of orthogonal polynomials on the unit circle whose Carathéodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of matrix Sylvester differential equations. For the particular case of semi-classical orthogonal polynomials on the unit circle, it is derived a characterization in terms of first order linear differential systems.info:eu-repo/semantics/publishedVersio

Structure relations for orthogonal polynomials on the unit circle

Structure relations for orthogonal polynomials on the unit circle are studied. We begin by proving that semi-classical orthogonal polynomials on the unit circle satisfy structure relations of the following type: [...]info:eu-repo/semantics/publishedVersio

Characterizations of Laguerre-Hahn affne orthogonal polynomials on the unit circle

In this work we characterize a monic polynomial sequence, orthogonal with respect to a hermitian linear functional [...]info:eu-repo/semantics/publishedVersio

Distributional equation for Laguerre- Hahn functionals on the unit circle

Let u be a hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding Carathéodory function. [...]info:eu-repo/semantics/publishedVersio

The organization of mathematics teaching at early years of the elementary school in Brazil

This article strives to describe the organization of Mathematics teach-ing at the early years of the Brazilian elementary education. It presents the structure of the curriculum, highlights main methodologies used in mathematics teaching at this level of school education as well as discusses the creation of textbooks in Brazi

Coherent pairs of linear functionals on the unit circle

In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. [...]info:eu-repo/semantics/publishedVersio

Coherent pairs of linear functionals on the unit circle

In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle: it is established that if ([mu]0,[mu]1) is a coherent pair of measures on the unit circle, then [mu]0 is a semi-classical measure. Moreover, we obtain that the linear functional associated with [mu]1 is a specific rational transformation of the linear functional corresponding to [mu]0. Some examples are given.http://www.sciencedirect.com/science/article/B6WH7-4S2MJ0D-1/1/61050bb3811832f373ff40a48b7461d