Abstract
The theory of a matrix-valued function Ω(ξ), j-elementary in the unit circle and having a pole at the point ς0, ¦ς0¦=1, on the boundary of the unit circle, is considered. The structure of Ω(ς) is determined, conditions for the splittingoff of Ω(ξ) from an arbitrary matrix-valued function W(ς), j-expanding in ¦ς|< 1, are formed, a theorem on the parametrization of a j-elementary matrix-valued function Ω(ς) of full rank is proved, and a decomposition of Ω(ς) of full rank into the product of parametrized j-elementary factors of full rank with simple poles at the point ς0 is found.
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Literature cited
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Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 62−74, 1988.
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Kovalishina, I.V. Theory of multiple j-elementary matrix-valued functions with a pole at the boundary of the unit circle. J Math Sci 49, 1280–1288 (1990). https://doi.org/10.1007/BF02209173
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DOI: https://doi.org/10.1007/BF02209173