Factorization of matrix functions and the resolvents of certain operators

Conceição, Ana C.; Kravchenko, Viktor; Teixeira, Francisco S.

http://hdl.handle.net/10400.1/14627

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Authors

Conceição, Ana C.

Kravchenko, Viktor

Teixeira, Francisco S.

Abstract(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).