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Factorization of matrix functions and the resolvents of certain operators
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Resumo(s)
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).
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Birkhäuser Basel