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- Factorization of matrix functions and the resolvents of certain operatorsPublication . Conceição, Ana C.; Kravchenko, Viktor; Teixeira, Francisco S.; Bottcher, A.; Kaashoek, M. A.; Lebre, A. B.; DosSantos, A. F.; Speck, F. O.The explicit factorization of matrix functions of the form Agamma(b) = ( (e)(b*) (b)(b*b)(+ gammae)), where b is an n x n matrix function, a represents the identity matrix, and gamma is a complex constant, is studied. To this purpose some relations between a factorization of A, and the resolvents of the self-adjoint operators N+ (b) = P(+)bP(-)b*P+ and N- (b) = P(-)b*P(+)bP(-) are analyzed. The main idea is to show that if b is a matrix function that can be represented through the decomposition b = b(-) + b(+) where at least one of the summands is a rational matrix, then it is possible to construct an algorithm that allows us to determine an effective canonical factorization of the matrix function A(gamma).
- Factorization of some classes of matrix functions and the resolvent of a Hankel operatorPublication . Conceição, Ana C.; Kravchenko, Viktor; Teixeira, Francisco S.; Samko, S.; Lebre, A.; DosSantos, A. F.The factorization of some classes of matrix-valued functions is obtained, which yields some new results for a special class of Hankel integral operators in L-2(+). For each of its elements, it is shown that the resolvent operator can be explicitly determined through a matrix factorization obtained by solving two non-homogeneous equations.