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Asymmetric factorizations of matrix functions on the real line. (English) Zbl 1120.47014

Erusalimsky, Ya.M. (ed.) et al., Modern operator theory and applications. The Igor Borisovich Simonenko anniversary volume. Basel: Birkhäuser (ISBN 3-7643-7736-4/hbk). Operator Theory: Advances and Applications 170, 53-74 (2006).
A classical right and asymmetric factorization for some classes of continuous matrix functions on the real line with a jump at infinity is obtained. The obtained results yield the existence of generalized inverses of matrix Wiener–Hopf plus Hankel operators and provide precise information about the asymptotic behavior of the factors at infinity and of the solutions to the corresponding equations at the origin.
For the entire collection see [Zbl 1104.47001].

MSC:

47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
15A23 Factorization of matrices
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
15A21 Canonical forms, reductions, classification
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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