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Distributional equation for Laguerre- Hahn functionals on the unit circle
Publication . Branquinho, A.; Rebocho, M. N.
Let u be a hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding Carathéodory function. [...]
On differential equations for orthogonal polynomials on the unit circle
Publication . Branquinho, A.; Rebocho, M. N.
In this paper we characterize sequences of orthogonal polynomials on
the unit circle whose corresponding Carathéodory function satisfies a Riccati differential
equation with polynomial coefficients, in terms of second order matrix
differential equations.
Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle
Publication . Branquinho, A.; Rebocho, M. N.
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.
Coherent pairs of linear functionals on the unit circle
Publication . Branquinho, A.; Foulquie-Moreno, Ana; Marcellan, Francisco; Rebocho, M. N.
In this paper we extend the concept of coherent pairs of measures from
the real line to Jordan arcs and curves. [...]
Characterizations of Laguerre-Hahn affne orthogonal polynomials on the unit circle
Publication . Branquinho, A.; Rebocho, M. N.
In this work we characterize a monic polynomial sequence, orthogonal
with respect to a hermitian linear functional [...]
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Entidade financiadora
Fundação para a Ciência e a Tecnologia
Programa de financiamento
SFRH
Número da atribuição
SFRH/BD/25426/2005