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Algebraic theory of multiple orthogonal polynomials
Branquinho, A.; Cotrim, L.; Moreno, A. FoulquiéIn this work we present an algebraic theory of multiple orthogonal polynomials. Our departure point is the three term recurrence relation, with matrix coefficients, satisfied by a sequence of vector multiple orthogonal polynomials. We give some characterizations of multiple orthogonal polynomials including recurrence relations, a Favard type theorem and a Christoffel-Darboux type formulas. An reinterpretation o...
Coherent pairs of linear functionals on the unit circle
Branquinho, A.; Moreno, A. Foulquié; Marcellán, F.; Rebocho, M. N.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...
Matrix interpretation of multiple orthogonality
Branquinho, A.; Cotrim, L.; Moreno, A. FoulquiéIn 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-ortogonality conditions. We state a Favard type theorem and the expression...
Dynamics and interpretation of some integrable systems via multiple orthogonal ...
Barrios Rolanía, D.; Branquinho, A.; Moreno, A. FoulquiéHigh-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 ...
Riemann-Hilbert problem associated with Angelesco systems
Branquinho, A.; Fidalgo Prieto, U.; Moreno, A. FoulquiéAngelesco systems of measures with Jacobi type weights are considered. For such systems, strong asymptotic development expressions for sequences of associated Hermite-Pad´e approximants are found. In the procedure, an approach from Riemann-Hilbert Problem plays a fundamental role. ; CMUC; FCT SFRH/BPD/31724/2006; UI Matemática e Aplicações from University of Aveiro
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