Abstract
We indicate a criterion for some classes of continuous matrix functions on the real line with a jump at infinity to admit both, a classical right and an asymmetric factorization. It yields the existence of generalized inverses of matrix Wiener-Hopf plus Hankel operators and provides precise information about the asymptotic behavior of the factors at infinity and of the solutions to the corresponding equations at the origin.
This article was started during the second author’s visit to Instituto Superior Técnico, U.T.L., and Universidade de Aveiro, Portugal, in February-March 2005.
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Dedicated to I.B. Simonenko on the occasion of his 70th birthday
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Castro, L.P., Duduchava, R., Speck, F.O. (2006). Asymmetric Factorizations of Matrix Functions on the Real Line. In: Erusalimsky, Y.M., Gohberg, I., Grudsky, S.M., Rabinovich, V., Vasilevski, N. (eds) Modern Operator Theory and Applications. Operator Theory: Advances and Applications, vol 170. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7737-3_4
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