Matrix Chebyshev polynomials and continued fractions

AbstractIn the first part we expose the notion of continued fractions in the matrix case. In this paper we are interested in their connection with matrix orthogonal polynomials.In the second part matrix continued fractions are used to develop the notion of matrix Chebyshev polynomials. In the case of hermitian coefficients in the recurrence formula, we give the explicit formula for the Stieltjes transform, the support of the orthogonality measure and its density. As a corollary we get the extension of the matrix version of the Blumenthal theorem proved in [J. Approx. Theory 84 (1) (1996) 96].The third part contains examples of matrix orthogonal polynomials