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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...
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...
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