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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Local and global factorizations of matrix-valued functions

Authors: K. F. Clancey and I. Gohberg
Journal: Trans. Amer. Math. Soc. 232 (1977), 155-167
MSC: Primary 47G05; Secondary 45E05
MathSciNet review: 0454742
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Abstract: Let C be a simple closed Liapounov contour in the complex plane and A an invertible $ n \times n$ matrix-valued function on C with bounded measurable entries. There is a well-known concept of factorization of the matrix function A relative to the Lebesgue space $ {L_p}(C)$. The notion of local factorization of A relative to $ {L_p}$ at a point $ {t_0}$ in C is introduced. It is shown that A admits a factorization relative to $ {L_p}(C)$ if and only if A admits a local factorization relative to $ {L_p}$ at each point $ {t_0}$ in C. Several problems connected with local factorizations relative to $ {L_p}$ are raised.

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Keywords: Operator factorizations, systems of singular integral equations
Article copyright: © Copyright 1977 American Mathematical Society

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