Page 46 - Textos de Matemática Vol. 34

36 AM´ILCAR BRANQUINHO
From this we get by integration the three term recurrence relation that {Pn} sat- isfies, and by Favard’s theorem we have that {Pn} is a matrix orthonormal poly-
nomials sequence.

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[2] S. Basu and N. K. Bose, Matrix Stieltjes series and network models, SIAM J. Math. Anal.
14 (1983), no. 2, 209-222.
[3] C. Brezinski, A direct proof of the Christoffel-Darboux identity and its equivalence to the
recurrence relationship, J. Comput. Appl. Math. 32 (1990), no. 1-2, 17-25.
[4] A. J. Duran, A generalization of Favard’s theorem for polynomials satisfying a recurrence
relation, J. Approx. Theory 74 (1993), 83-109.
[5] A. J. Duran and P. Lopez-Rodriguez, Orthogonal matrix polynomials: Zeros and Blumen-
thal’s theorem, J. Approx. Theory 84 (1996), 96-118.
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Am´ılcar Branquinho, Departamento de Matema´tica, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal
E-mail address: ajplb@mat.uc.pt