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On the relation between the full Kostant-Toda lattice and multiple orthogonal p...

The correspondence between a high-order non-symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving explicit expressions for the resolvent function and, under some conditions, the representation of the vector of functionals, associated with the solution for our integrable syste...

Dynamics and interpretation of some integrable systems via multiple orthogonal ...

High-order non-symmetric difference operators with complex coefficients are considered. The correspondence between dynamics of the coefficients of the operator defined by a Lax pair and its resolvent function is established. The method of investigation is based on the analysis of the moments for the operator. The solution of a discrete dynamical system is studied. We give explicit expressions for the resolvent ...

Matrix interpretation of multiple orthogonality

In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials.We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present a matrix interpretation of the type II multi-orthogonality conditions.We state a Favard type theorem and the expression ...

Riemann-Hilbert problem associated with Angelesco systems

Angelesco systems of measures with Jacobi-type weights are considered. For such systems, strong asymptotics for the related multiple orthogonal polynomials are found as well as the Szego-type functions. In the procedure, an approach from the Riemann Hilbert problem plays a fundamental role.

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. Some examples are given.

Normal indices in Nikishin systems

We improve the class of indices for which normality takes place in a Nikishin system and apply this in Hermite-Padé approximation of such systems of functions.

Contribuições de Vicente Gonçalves na teoria dos polinómios ortogonais

Problemas Inversos na Teoria dos Polinómios Ortogonais

O problema em que trabalhámos foi o de obter a medida associada a uma dada sucessão de polinómios ortogonais, conhecida uma representação para os coeficientes da relação de recorrência a três termos que sabemos verificarem estas sucessões. Este tipo de problemas são conhecidos na literatura como problemas inversos. Dividimos o nosso trabalho em três partes. Na primeira, expomos as noções gerais da teoria dos po...

Polinómios ortogonais e funcionais de momentos : problemas inversos

Dissertação do mestrado em Matemática apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra